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Xerox University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 75-6533 LONG, Larry Eugene, 1945- A PRIORI PREDICTION OF AN INDIVIDUAL'S HEART RATE RESPONSE TO A SERIES OF PHYSICAL TASKS OF VARYING LEVELS OF WORK LOAD. The University of Oklahoma, Ph.D., 1974 Physiology
Xerox University Microfilms, Ann Arbor, Michigan 48io6
© 1974
LARRY EUGENE LONG
ALL RIGHTS RESERVED
THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. THR UNIVERSITY OF OKLAHOMA
GRADUATE COLLEGE
A PRIORI PREDICTION OF AN INDIVIDUAL'S HEART RATE RESPONSE
TO A SERIES OF PHYSICAL TASKS OF VARYING
LEVELS OF WORK LOAD
A DISSERTATION
SUBMITTED TO THE GRADUATE FACULTY
in partial fulfillment of the requirements for the
degree of
DOCTOR OF PHILOSOPHY
BY
LARRY E. LONG
Norman, Oklahoma
1 9 7 4 A PRIORI PREDICTION OF AN INDIVIDUAL'S HEART RATE RESPONSE
TO A SERIES OF PHYSICAL TASKS OF VARYING
LEVELS OF WORK LOAD
APPROVED BY
jlM fljLiC N J .
LJh<û<ùe^. DISSERTATION ZOLTUTTEE ABSTRACT
A PRIORI PREDICTION OF AN INDIVIDUAL'S HEART RATE RESPONSE
TO A SERIES OF PHYSICAL TASKS OF VARYING
LEVELS OF WORK LOAD
By: Larry E. Long Chairman: LaVeme L. Hoag
This dissertation presents the development of a pre dictive model for depicting an individual's cardiac response to a series of adjacent fixed intensity tasks. The emphasis is on predicting cardiac response to exercises of no more than four minutes duration.
The most apparent deterrent to predicting heart rate patterns, caused by work onset or stoppage, is the extreme variation in absolute heart rate between individuals. How ever, this variation can be substantially reduced by trans lating heart rate in beats/minute to a percent of an individ ual's average resting heart rate (%RHR). The translation provides a common denominator and thereby a common origin ror heart rate patterns produced by different individuals.
It was determined that cardiac responses in terms of percent of resting heart rate were similar for selected sub ject categories. The subject categories of this study are defined by two levels each of sex and physical fitness. A highly correlated linear relationship between work load and steady state %RHR was developed for each of the four subject categories. Cardiac responses in terms of ^RHR were empir ically derived for set levels of %RHR. The linear relation- sliips and responses in %RHR constitute the foundation of the preflic t ive model. The predictive model functions by extrapo lai j.ng I» heart rate response to exercise from empirically derived data. The only required inputs are sex, physical fitness, and resting heart rate. The output of the model includes the predicted "oRHR and the predicted heart rate. TJie model will predict the cardiac response to a series of step changes in work load within the limits of 100 to l60 %RHR. Ninety percent of the time, the predictive model was shown to be within 5 to 10% of the observed heart rate pat tern.
Ill ACKNOWLEDGEMENTS
I -would like to express gratitude to the professors on my doctoral committee for their contribution towards the successful completion of this dissertation, which would have not been possible without their able direction. Dr. Arnold
Parr served as a personally interested and constructively critical committee member from outside the Department of
Industrial Engineering. The observations of Dr. Hillel Kumin and Dr. B. L. Foote supplied needed insight into the interdis ciplinary ramifications of this study. Dr. Jerry Purswell worked very closely with my chairman in defining the scope of the study and rendered invaluable expertise throughout the course of the investigation. I am especially appreciative of the technical assistance and guidance of my committee chairman, Dr. LaVerne L. Hoag. He gave willingly of his time and offered continual encouragement and moral support.
I would like to thank all of the people who served as subjoc(s. Everyone was a willing participant and devoted
long liom's during the testing phase. Also, I am grateful for t he £idm i nis t rat ive and financial assistance afforded by the
School of Industrial Engineering. Ms. Marty Peters deserves a special thanks for typing the manuscript.
I met my wife, Nancy, on the day that I began work
XV towards a doctorate. Since that day, she has been the per pétuant behind my pursuance of this objective. I wish to thank her. Nancy has also contributed directly in the com pletion of this study by serving as experimental and admin istrative assistant, subject, typist and editor. TABLE OF CONTENTS
Page
LIST OF TABLES ...... viii
LIST OF ILLUSTRATIONS ...... x
Chapter
I. INTRODUCTION ...... 1
Statement ol' Problem ...... 1 Relevance and Contribution ...... 13 Uses of Heart Rate Patterns ...... I6
II. RELATED INVESTIGATIONS AND RESEARCH .... l8
General Background ...... l8 Initial Value of Heart Rate Consideration . 26 Training and Its E f f e c t ...... 29 Predictive Models for Heart Rate ...... 30
III. THE EXPERIMENT ...... 40
General Description of Experiments ...... 40 Industrial Applicability of the Experiment . 42 Experimental Apparatus ...... 44 S u b j e c t s ...... 48 Experimental Procedures ...... 53 Collection of Heart Rate Data from Recorded Output ...... 6l
IV. THE EXPERIMENTAL DESIGN AND PREDICTIVE MODEL 64
The Experimental Design for Data Collection 64 The Predictive Model ...... 66
V. ANALYSIS OF R E S U L T S ...... 94
Regression Analysis of Work Load t o Steady State % R H R ...... 94 Analysis of Hard Data Patterns ...... 102 Comparison of the Accuracy of Various Predictive Models ...... 126 vi Page
Evaluation of Predictive Model ...... 139
VI. CONCLUSIONS AND R E C O M M E N D A T I O N S ...... l6?
Conclusions ...... 1^7 Recommendations for Continued Studies . . . 170 S u m m a r y ...... 17^1
BIULIOGRAPHY ...... 176
APPENDIX 1 ...... 179
APPENDIX ...... 182
APPENDIX 3 ...... 184
APPENDIX 4 ...... 189
APPENDIX 5 ...... 195
APPENDIX 6 ...... 198
APPENDIX 7 ...... 199
APPENDIX 8 ...... 212
APPENDIX 9 ...... 223
APPENDIX 1 0 ...... 224
APPENDIX 1 1 ...... 225
APPENDIX 1 2 ...... 226
APPENDIX 1 3 ...... 227
APPENDIX l 4 ...... 228
vix LIST OF TABLES
Tabic Page
1. Subject Categories ...... 52
2. Matrix of Experimental Step Changes in Task I n t e n s i t y ...... 58
3 . Sources of Variation, Associated Degrees of Freedom, and Denominator of the F-Ratio . . . 67
k. Format of Data Collection S c h e m e ...... 68
5 . Nomenclature for Hard Data Patterns ...... ?1
6. Combinations of Possible Step Changes in %RHR for P ...... 77
7 . Output of Predictive Model for Series of Fixed Intensity Tasks of the Numeric Example .... 93
8. Data for Work Load to Steady State %RHR Relationships by Subject Category ...... 97
9 . Critical and Computed Values of "F" for Test ing Standard Errors ...... 99
10. Critical and Computed Values of "t" for Test ing Regression Coefficients ...... 99
11. ANOVA Summary ...... 104
12. Comparison of Predicted Heart Rate Patterns Using Hard Data Patterns by Subject Category and by using Averaged Hard Data Patterns . . . 124
1 3 . Predicted and Observed Cardiac Responses for Series 3 - M G ...... I3I
14. Predicted and Observed Cardiac Responses for Series 3 - M S ...... 132
1 5 . Predicted and Observed Cardiac Responses for Scries 3 - l ' " G ...... 133
viii Tablo Page
1 6 . Predicted and Observed Cardiac Responses for Series 3—F S ...... 134
1 7 . Exercise Series for Validation Testing ...... l40
1 8 . Histograms and Descriptive Statistics for Time P e r i o d s ...... 1^5
1 9 . Histograms and Descriptive Statistics by Series for MG and M S ...... l48
20. Histograms and Descriptive Statistics by Series for FG and F S ...... l49
IX LIST OF ILLUSTRATIONS
Figure Page
1. Example of relationships between steady state heart rate, %RHR, and work load .... 8
2. Heart rate patterns (heart rate vs. time) for tasks of light intensity ...... 10
3. Heart rate patterns (/’oRHDR vs. time) for tasks of light i n t e n s i t y ...... 10
4. Heart rate patterns (heart rate vs. time) for tasks of moderate intensity ...... 12
3. Heart rate patterns (%RHR vs. time) for tasks of moderate intensity ...... 12
6 . Heart rate curves during exercise and recov ery for increasing work intensities ...... 20
7. Expected relationship between response and recovery to exercise ...... 2?
8 . Example heart rate patterns for varying ini tial heart rate values for tasks of fixed i n t e n s i t y ...... 28
9. Recording equipment ...... 4?
10. Subject exorcising on bicycle ergometer . . . 4?
11. Strip chart recorder output ...... 62
12. Selection process for high and low heart rate p a t t e r n s ...... 79
1 3 . Graphic example of derivation of predicted heart rate pattern ...... 89
14. Graphic example of derivation of predicted heart rate pattern for recovery to a resting s t a t e ...... 91
X Figure Page
15- Steady state /'oRliR versus work load rela tionships for all subject categories .... 96
1 6 . Work load to steady state %RHR and heart rate for MG and M S ...... 101
1 7 . Plot of Sex Effect for Task A3 ...... IO6
1 8 . Plot of Physical Fitness Effect for Task A3 IO7
1 9 . Plot of Physical Fitness Effect for Task A4 108
20. Physical fitness-sex interaction for Task A 4 ...... 110
21. Physical : fitness-se X interaction for T ask B4 . . . 111
22. Plot of Physical Fitness Effect for Task 01 112
2 3 . Plot of Sex Effect for Task C4 . 114
24. Hard data patterns--Task A2 . . 115
2 5 . Hard data patterns--Task A3 . . 115
2 6 . Hard data patterns--Task A4 . . 116
2 7 . Hard data patterns--Task B1 . . 116
2 8 . Hard dat a patterns- —T a sk B3 . . 117
2 9 . Hard data pat terns- -Task B4 . , 117
3 0 . Hard data pattems--Task Cl . . 118
31. Hard data patterns- —Ta sk 02 . . 118
3 2 . 1 Icird dat a pat terns- -Task 04 , 119
33. 1 lard da ta pat t erns- —Task D1 . . 119
3'i. Hard data patt erns--Task D2 . . 120
3 5. Hard data pat t erns--Task D3 . . 120
3 6 . Histogram showing distribution of error over all time periods and all series 142
XX Figure Page
37• Plot of predicted and observed heart rate responses for series 1-MG ...... 153
3O. Plot of predicted and observed heart rate responses for series 2-MG ...... 153
39- Plot of predicted and observed heart rate responses for series 3- M G ...... 15^1
40. Plot of predicted and observed heart rate responses for series 4—M G ...... 154
41. Plot of predicted and observed heart rate responses for series 5-MG ...... 155
42. Plot of predicted . i..d observed heart rate responses for series 6-MG ...... 155
4 3 . Plot of predicted and observed heart rate responses i'or series 1-MS ...... 157
44. Plot of predicted and observed heart rate responses for series 2-MS ...... 157
4 5 . Plot of predicted and observed heart rate responses for series 3-MS ...... 158
46. Plot of predicted and observed heart rate responses for series 4—M S ...... I58
4 7 . Plot of predicted and observed heart rate responses for series 5-MS ...... 159
48. Plot of predicted and observed heart rate responses for series 6 - M S ...... 159
4 9 . Plot of predicted and observed heart rate responses for series 1-FG ...... I60
5 0 . Plot of' predicted and observed heart rate es pons es for series 2—F G ...... 16O
51. Plot of predicted and observed heart rate responses for series 3- F G ...... I6I
52. Plot of predicted and observed heart rate responses for series 4-FG ...... I61
53» Plot of predicted and observed heart rate responses for series 5-FG ...... I62
Xll F j g;iiro Pago
5^1. Plot of predicted and observed heart rate responses for series 6-FG ...... l62
55- Plot of predicted and observed heart rate responses for series 1- F S ...... l64
5 6 . Plot of predicted and observed heart rate responses for series 2-FS ...... l64
57- Plot of predicted and observed heart rate responses for series 3- F S ...... 165
5 8 . Plot of predicted and observed heart rate responses for series 4- F S ...... I65
1 9 . Plot of predicted . nd observed heart rate responses for series I66
6 0 . Plot of predicted and observed heart rate responses for series 6-FS ...... 166
xixx A J’RIORI PRRDJCTTON OF AN INDIVIDUAL'S HEART RATE RESPONSE
TO A SERIES OF PHYSICAL TASKS OF VARYING
LEVELS OF WORK LOAD
CHAPTER I
INTRODUCTION
The introductory chapter contains definitions of the terminology unique to this study, illustrations and examples of the problem and the predictive model of this investiga tion, a discussion of the relevance and contribution of this study, and a discussion of the uses of heart rate pat terns.
Statement of Problem
The purpose of this study was to develop a predic tive model of an individual's heart rate response over time as he performs physical tasks of fixed intensity for varying levels of work load. The emphasis is on short- range patterns of no more than four minutes for tasks of light to moderate intensity (less than 220 watts). The tasks are of a constant mechanical power. As long as the work load or power output requires less than approximately
'jO percent of an individual's aerobic capacity, the heart rate will reach a steady state (SS) (Vogt, 1973, p. 46). 2
The intensity of the work loads of all tasks are such that
the heart rate will reach a steady state in aerobic metab
olism.
It is difficult to predict an individual's cardiac
response to physical stress in terms of heart rate (heart
rate pattern) because individuals have such disparate
heart rate patterns for any given work load. For example,
given a work load (task) of 50 watts, one individual's
heart rate may reach a steady state of 80 beats/minute in
10 seconds while another individual may take 30 seconds
and steady state at 100 beats/minute. These patterns can
be studied universally by introducing compensatory varia
bles and by the reduction of heart rate to a common denom
inator. This common denominator is percent of resting
heart rate (%RHR) and is a function of each individual's
resting heart rate (RHR) and his heart rate under physical
stress.
For the purposes of this study, a person's resting heart rate is determined after he has been seated for at
least 15 minutes. Resting heart rate is determined by
counting the number of beats/minute during a 5-minute per
iod following 15 minutes of rest to determine the average beats/minute at rest or the resting heart rate. When
determining a subject's resting heart rate the subject
should not eat nor exercise for at least one hour prior to
testing. An unofficial study was conducted for the purpose 3
of establishing resting heart rate as a physiological
index with perennial stability. The medical records of twenty Air National Guard flying personnel, selected at random, were examined. The selected resting heart rate was recorded for each individual on a yearly basis during routine medical examinations performed by National Guard physicians for five to fifteen years depending upon the history of their individual medical records. It was deter mined that the resting heart rate exhibited perennial sta bility. The average standard deviation for all persons examined was approximately four beats/minute. This differ ence could very easily be attributed to variations in the clinical procedures used to determine resting heart rate.
It is expected that there are several variables which affect the increase or decrease, rate of increase or decrease, and/or level of heart rate. The extent of tlie effect of any given variable is unknown. Also, it is prob able tliat as the level of one variable is changed in combi nation with another variable, that variable may have an altogether different effect on an individual's cardiac response to exercise (i.e., interaction effect). Environ mental variables which might be considered to have an effect on cardiac response to exercise are:
1. temperature
2. humidity
3. noise level. 4
Human variables which might be considered to have an effect
on cardiac response to exercise are:
1. somatotypes
2. extent of body movement
3. endurance capabilities
4. psychological stress
5. maximum heart rate level
6. maximum oxygen uptake
7. muscle mass
8. heart rate variability
9. body temperature
10. stroke-volume
11. age
12. resting heart rate
13* physical fitness l4. sex.
The latter three, resting heart rate, physical fitness, and
sex, were examined for this study. These were chosen
because persons can be classified by sex,and resting heart
rate can be measured easily. As discussed in a later sec
tion under subject variables, an individual
classified into an appropriate level of physical fitness.
Also, it is known that all three variables have a consider
able effeci on hear t rate patterns. During testing, con
trols were established to minimize variation within all
other variables listed above. The subjects were limited 5 to the age group of 20 to 30 years of age. Studies have shown that some of the above environmental and human vari ables listed have an effect on heart rate, and it is tiypo- thesized that others may have an effect on heart rate.
However, the extent of this study is to develop a model by which heart rate patterns can be predicted given only levels of sex, physical fitness and resting heart rate.
There are two levels of sex and physical fitness. The levels of sex are male (M) and female (F). The levels of physical fitness are good physical fitness (G) and seden tary (S). Resting heart rate is not a factor in defining sul),ject categories. Consequently, there are four subject categories. Those categories are male of good physical fitness (MG), sedentary male (MS), female of good physical fitness (FG), and sedentary female (FS). The levels of the variables and the subject categories are discussed in detail in Chapter TTI.
This study is limited in scope to examining only aerobic tasks for all subjects. Sstrand (1970, p. 283) states that exercises requiring an anaerobic energy contri bution are those that demand more than 50 percent of an individual's maximal aerobic power. He also presented the steady state heart rate for different age groups for 50 percent of maximal aerobic power for both males and females (Sstrand, 1971, p . 312). These maximum heart rate values for aerobic exercise for the age group of this study 6 were 1]4 and I38 beats/minute for males and females, respectively. The limits of this study are from 100 to
160 %KHJÎ; therefore, the maximum allowable resting heart rate for subjects was 84 beats/minute for males and 86 beats/minute for females in order that no task would require an anaerobic contribution and that a steady state heart rate could be achieved for all tasks performed by all subjects.
It was shown (in this study) that individuals of similar characteristics (e.g., males of good physical fit ness) have similar heart rate patterns when presented as
%R1IR versus time. It was also apparent that although a specific heart rate pattern can be produced by persons of all subject categories, the actual mechanical work necessary to produce this pattern varies for each subject category.
There is little value in predicting a heart rate pattern if it is necessary to supply the expected steady state heart rate as input to the model. If this were the case, it would be necessary to empirically determine the steady state heart rate for a given task for any given individual.
Upon considering tlris need, it becomes apparent that in order (o make heart rate patterns a useful tool for indus-
(î'ia.1 use, any given heart rate pattern must be equated with a work load. It was hypothesized at the onset and later determined experimentally that the relationship between work load and steady state %RHR is linear and unique for each subject category over the range of this 7 study (100 %HHR to l60 % RHR).
The immediate problem in predicting heart rate pat terns is the extreme variation in absolute heart rate (HR), even for persons of similar characteristics (same subject category). A relationship between work load and steady state heart rate such as shown in Figure 1 can be developed.
However, the only way to develop this relationship is to record steady state heart rate at different levels of work loads for each individual separately. A similar relation ship could be developed by using averaged data supplied by a group of subjects. However, one standard deviation about the regression line may be as much as 15 beats/minute.
Therefore, it is difficult to draw conclusions about indi viduals from relationships developed from averaged data because of the individual variations attained in absolute heart rate. There is also a need to eliminate the require ment to empirically determine the work load versus steady state heart rate relationship for each individual. Per haps the key to examining this relationship is to reduce all relationships to intercept at a common point. This can be accomplished by using percent of resting heart rate (%RHR) instead of heart rate. Regressions for work load versus steady state %RHR were computed for all subject categories from empirical data. These relationships serve as input to the model. Therefore, given a work load and category of subject, the expected steady state %RHR can be determined. 8
200.
/ / 150 iBo- / /
160 l40 Q) -P (C Qh I « 140' « X 130 % Q) -p 4-> m (S % X W 120' tc m
(0 120 ^ 0) ^ 1 0 0 .
110 80
60 100
I— ■■, ■ .1 . .f IIii.i. , I ..I—... r- -n 0 50 100 150 200 250 W o r k Load (-watts)
Figure 1 . Example of relationships between steady state heart rate and w o r k load (solid line— left ordi nate) and between steady state %RHR and work load (dotted line— right ordinate). 9
I'Lgure 1 also illustrates the relationship between work
load and steady state %RHR.
The heart rate pattern is defined, for the purposes
of this study, as an individual's heart rate over time from
the instant he begins performing a physically demanding
task of fixed intensity (including the resting state) until
the termination of the task. The instant the individual
stops performing a task of fixed intensity and begins a
different level of fixed intensity (could be a resting
state), another heart rate pattern is realized. In this
case, a step change in work load or task intensity is realized. Figure 2 illustrates graphically what is meant
by a heart rate pattern. Shown are the resultant heart rate patterns of two subjects who each performed a light work task. Subject A is of the sedentary male subject category and Subject R is of the sedentary female subject category. Tlie task intensity was not the same. It can be noted that there was a 10 beat/minute difference in the
initial heart rate values (in this case resting heart rate) at time zero. Subject A realized a steady state heart
rate at 93 beats/minute after 48 seconds and Subject B at Bo beats/minute after 53 seconds. It would be difficult
to predict these heart rate patterns since it is possible and probable that another subject of Subject A's character
istics (sedentary male--MS) could have produced Subject B's
( sedentary I'eniale — FS) heart rate pattern and vice versa. 1 0
HO
10 20 30 40 50 60 70
Time (aec)
Figure 2. HR patterns (HR versus time) for two subjects performing tasks of light intensity.
140
130
170 S u b jtc t A
110
100
iO
I I r « ( •
Figure 3. HR patterns (%RHR vs time) for two subjects per forming tasks of light intensity. 1 1
Figure 3 illustrates the graphic representation when ‘’uFllU is used instead of heart rate to indicate heart rate pat terns. Note that although the heart rate patterns are similar, the level of work load or task intensity at a steady state of 133 %HHR is not necessarily the same. The task intensities were 125 watts and 70 watts for Subjects
A and H, respectively. Figure 4 illustrates, again, the disparity in heart rate patterns for tasks of moderate intensity (versus light intensity for Figure 2). The heart rates of both subjects reach a steady state at l60 %RHR as sJiown in Figure 5» However, again the task intensities required for like levels of steady state %RHR were differ ent. The task intensities were 220 watts and 130 watts for Subjects A and B, respectively.
in order to illustrate the method by which the predictive model of this study compensates for the dispar ity in work load for similar patterns (of %RHR), the fol lowing example is presented. An individual is selected from one of the four subject categories. The individual is a sedentary male (MS) and his seated resting heart rate is ~('i boa ( s/mi nu I, e. The intensities and durations of the laslcs must Ixr supplied. I'or example, the model will pre dict tlie heart rate response for a series of tasks of 110 watts for G o seconds, 175 watts for 70 seconds and zero watts for 110 seconds. By using Figure 1 as the steady state '/'(RHH to work load relationship for sedentary males. 1 2
III)
lÜU
so
70
bO
0 10 20 30 60 50 t-.9 70
T im e (see) Figure 4. HR patterns (HR versus time) for two subjects performing tasks of moderate intensity.
160
150
160
Subje ct A no . Subject r.
120
ini)
70 Time (sec) I' IKure 5* HR patterns (%RHR vs time) for two subjects per forming tasks of moderate intensity. 13
it can be determined that there are steady state ‘’oRIIR's of 130, l4y, and 100 for work loads of 110, 175, and zero watts, respectively. The model supplies all transient responses between step changes in task intensity. This procedure is explained in detail in Chapter IV. The model predicts in terms of %RHR and then %RHR is translated to heart rate, since the individual's resting heart rate is given. The results of the predictive model for the subject and series of tasks previously defined are shown in Appen dix 7 under series 1-MS.
Relevance and Contribution
Upon reviewing the papers presented at a symposium on heart rate variability, Rolfe (1973, p* 2) stated:
It will be widely acknowledged for those who have mea sured heart rate variability that an anomaly frequently presents itself ; namely that while a recorded trace of HR often shows clearly the suppression of variability in the work condition, it is difficult to quantify the change in cardiac response and relate it to the task. This theme is apparent throughout the papers which follow. The study of HR variability is at the stage where the problem is no longer one of getting effec tive electrodes and portable cardiac recording apparatus; rather it is in the development of techniques to process and analyze the data.
At present, no one has developed a predictive model which reflects cardiac response to stimuli on an individual basis.
Aberg, Elgstrand, Magnus and Lindholm (I968, p. 189) collaborated in an attempt to build a model to predict energy expenditures. (HR has been shown to be an effective predictor of energy expenditure (LeBlanc, 1957, p. 275).) 14 Their rationale for building this model merits repeating.
The accuracy of physiological work studies depends only in part on the measuring instrument itself. If the measurement is performed on work which is insuf ficiently described, the total accuracy of the mea surement is decreased. A proper selection of descrip tion variables increases the accuracy of physiological work measurement and makes a fairly general prediction of the energy expenditure possible. A model for pre diction of energy expenditure from physical data is proposed and has been tested in a number of industrial cases. The accuracy of the result is of the same order of magnitude as a good work study.
They indicate that a good predictive model can produce results which are as accurbe, in many cases, as if actual measurements were taken. The advantages of predictive mod els becomes readily apparent when it is recognized that it is possible to produce a heart rate pattern of the same order of accuracy as that of an empirical investigation.
The predictive model of this study has the potential to produce the heart rate pattern for any individual which fits a combination of the levels of the two variables investigated (e.g., female of good physical fitness). An individual's cardiac response to tasks requiring certain steady state %RlIRs can be depicted without actual measure ment of heart rate while performing these tasks. This could result in savings in time and resources to industrial and government organizations.
1/Ucien Brouha (196O, p. 15), who was an established autliority in physiological stress in industry, stated:
Ln man, research is limited by the methods that can be used without impairing the subject's health or his performance. This consideration reduces substantially 13
the kind of measurements that can be made directly during muscular activity. Fortunately, because of its close relationship to cardiac output and oxygen con sumption, heart rate can be utilized to evaluate stress imposed by muscular activity with a minimum amount of interference with the subject's freedom of motion and performance ability. As a single factor, it can quite accurately depict the adjustment of the individual to muscular work and can be used conveniently as an index for evaluating the overall adaptation to muscular activ ity.
As Brouha indicated, heart rate is a viable tool for measur ing muscular activity. However, interpretation of individual heart rate patterns is difficult with the present knowledge.
Heart rate and heart rate patterns may vary greatly between sex, physical fitness, etc.; however, the predictive model ing technique developed within this study aids in trans forming disparate heart rate patterns into comparable terms.
Man has physical limitations such as endurance and strength which are approached and sometimes surpassed in his working environment. These limitations must be recog nized as critical when establishing criteria for work standards. An individual's heart rate could be a valuable tool when correlated with other limited physical capacities
(e.g., endurance capabilities, blood pressure, work capacity, etc.). An investigation of heart rate patterns could provide the necessary information required to depict why and how an individual's heart rate varies. If so, then standards could be established for undue stress to not only the individual's cardiovascular system, but also other limited physical capabilities. 16
Uses of Heart Rate Patterns
The predictive model utilizes heart rate patterns to depict the expected cardiac response of an individual to physical work tasks of varying intensity. By accur ately predicting the cardiac response to work tasks the need for actual measurement of an individual's heart rate under physical stress would be eliminated.
At this time specific guidelines have not been estab lished to set critical limits of heart rate for individuals of specific categories with respect to %RHR. At present, heart rate and/or oxygen consumption are used for industrial guidelines to measure physiological cost. However, only unofficial guidelines exist, and then, only average values are presented. For example, gross unofficial guidelines are that a worker not be required to work on a continuous basis at a rate of over 4.5-5 kcal/min for metabolic energy expenditure and/or 120-125 beats/minute for heart rate.
It is difficult to apply such guidelines since energy expenditure and heart rate vary so greatly between indivi duals. Murrell (1965, p. 375) compared two men of different size to illustrate this difference. A l44-pound male expended 4.0 kcal/min of work where a 200-pound male expended 5.3 kcal/min of work while walking at a rate of
3 mph. The former was within the unofficial guidelines and the latter was above, yet both were accomplishing the same task. This illustration points out the need for 17 individualizing guidelines for energy expenditure and heart rate.
Future guidelines might reflect critical limits for %RHR for particular categories of individuals. From this study, and under the restrictive conditions of this study, a task requiring a particular physical work output could he applied to each subject category (within this study). Then the task could be related to a steady state
%RHR for each subject category. For example, a steady state of 150 %RHR might be the standard maximum allowed for an 80 watt task of 5 minutes duration. (These criteria will have to be determined in a subsequent study.) It could also be true that only males of good physical fit ness between the ages of 20 and 30 can maintain a steady state %RHR of less than I50 %RHR for that task. In this case, only persons of that category would be allowed to perform this task. All other tasks could be evaluated in a similar manner; therefore, the proper worker would be placed in the proper working environment.
In summary, this model allows for the collection and evaluation of heart rate data in comparable forms
(%RHR). A national program to develop a historical data bank of cardiac responses (in terms of %RHR) of individuals of various personal characteristics for various task inten sities could result in work standards. These standards could be effectively used for personnel selection and task evaluation. CHAPTER II
RELATED INVESTIGATIONS AND RESEARCH
This investigation encompasses an attempt to develop a predictive model for cardiac response to fixed intensity tasks which can be related to the individual. There are many research efforts which have supplied direction and foundation for this examination. Of particular importance are the past attempts to develop predictive models. Research efforts pertinent to the development and evaluation of this model are presented in this chapter.
General Background
LeBlanc (1957» p. 275) indicates that heart rate can be an effective tool in the measurement of work activities.
It had been determined by several experimentcrc- that there is a definite correlation between heart rate and oxygen consump tion within a limited range. LeBlanc extended his studies to investigate work and recovery heart rates of individuals while exercising at different levels of activity. He was concerned with curves which showed the heart rate pattern for one par ticular exercise. First, he illustrated graphically the pat tern from resting heart rate to termination of a one mile run while varying the intensity (speed of runner). Second, he
18 19 illustrated the pattern from resting heart rate to termina tion of a run which extended for varying lengths of time.
The heart rate pattern showed an upward trend as intensity and/or duration was increased. It was apparent that the body experienced fatigue, therefore the heart rate increased to exhaustion at high levels of intensity and duration.
LeBlanc also viewed the associated recovery patterns.
Since the body seemed to fatigue, he suggested that heart rate be used as an index of level of fatigue. Although it is not within the scope of this study to investigate fatigue, the results do indicate that the transient heart rate response to a step increase in work load as well as the recovery heart rate patterns are good indicators of physical fitness.
Brouha (196O, pp. 15-1?) depicted the types of heart rate patterns (he used the term heart rate curves) for exer cise situations into three categories. The first is where an individual is subjected to light exercise. The cardiac reac tion to this light exercise is exaggerated at first but then gradually decreases to a steady state which is above the nor mal resting heart rate. The second curve involves a more intense exercise during which the heart rate increases to a steady state. The third curve is when the exercise intensity is such that the heart rate does not reach a steady state but continues to increase until the individual is exhausted.
Figure 6 illustrates Brouha's "three typical curves."
Empirical results collected by this writer indicate 2 0
III 160
140 II
'a E 120 m -p ITS 0)
100 0) -p (0 a
-p u (0 o 80
Exercise Recovery 60
0 5 10 15 20 25 Time (min)
Figure 6. Heart rate curves during exercise and recovery for increasing work intensities. (Brouha, I96O, p. 16) 2 1 a deviation from these typical curves. With respect to the first curve, there was not so much increase above steady state heart rate at the start of the task. There was, instead, a gradual increase in heart rate to steady state.
The second curve can also be challenged as to its general validity and application to any given individual. The graph of Figure 6 indicates that an individual with a resting heart rate of 75 beats/minute will maintain a heart rate of
130 beats/minute for an exercise of sufficient intensity to cause the cardiac effect of Curve II, for 15 minutes or longer. Fifteen minutes is a very long time to maintain a steady state for such an intense exercise. The results of experiments conducted by this writer indicated a very gradual increase after approximately three to four minutes for heart rates of 130 beats/minute as body fatigue became a factor.
The 130 beats/minute is the approximate maximum heart rate of all subjects attained during experimentation (maximum
134 beats/minute). The third curve indicates an increase to exhaustion. An individual may reach a steady state (maximum attainable heart rate) prior to exhaustion and continue the exercise. Exercise of this intensity could be harmful to certain individuals' health and should be avoided.
Authorities such as Brouha (I96O, pp. 17, 19, 8 9 , 111) and Murrell (1965, p. 376) have tended to study heart rate patterns in a gross form utilizing heart rate averages of many persons to display results and depict transient responses. 22
It is common among researchers to display heart rate pat terns graphically by plotting average heart rate against time; however, much information is lost when averaging the heart rates of many persons. For example, it is possible that the resting heart rates of a group may range from 56 to 90 beats/minute with an average of 78 beats/minute. The individual with a resting heart rate of 56 beats/minute may never exceed the average of 78 beats/minute for a light work task. This information is lost in the average.
An alternative to displaying heart rate patterns was shown by Schilpp (1951» P* 44l). He utilizes beats/minute above resting heart rate in order to represent a general heart rate pattern. The assumption which is implied, but is not not ed by Schilpp, is that each individual engaged in muscular ac tivity will have the same increase in heart rate and the increase is independent of an individual's resting heart rate. As Brouha
(i960, p. 22) notes, the resting heart rate is an indication of physical fitness, and therefore the heart rate displacement
(beats/minute above resting heart rate) can be expected to be less for an individual with a lower resting heart rate.
The results of this dissertation indicate that heart rate patterns produced by dynamic muscular activity of fixed intensity can be reproduced as the individual repeats the exercise. However, the repetition of a pattern is dependent on the intensity of work and the duration of the preceding rest period. Approximately the same heart rate pattern can be obtained from an individual performing successive trials
of the same task if the rest period is of sufficient duration.
Rest periods are, in practice, not long enough for any indi
vidual to completely recover from an intense work task (20
minutes to over an hour). There is an accumulative effect
which causes dissimilar heart rate patterns to occur when an
individual is subjected to a task without sufficient rest.
For light and moderate work loads the heart rate pattern can
be repeated with accuracy. Even though a subject may be a
little fatigued, an approximate replica of the heart rate pat
tern will still be produced when the task is light to mod
érât e.
One objective of this study was to isolate and describe
the effects which certain variables (sex and physical fitness) have on the heart rate of an individual under a controlled
environment. It has been established that humidity and temp
erature do appreciably affect the heart rate during exercise
(Brouha, Smith, DeLanne, Maxfield, 196O, p. 137). These two
factors will not be examined. In the same study, the authors
did pinpoint sex as a definite variable to be examined. They
determined the reactions of females to be similar but at a
statistically significant higher level than men. Under exer
cise conditions in a controlled environment the average female
subject's heart rate is 6 to 8 beats/minute higher than a
male's. This deviation in heart rate between the sexes is
considerable; therefore, sex i included as a variable in the 2 h
predictive model of this study.
Related, perhaps, to studying the heart rate pattern
is the study of heart rate variability. Malmo and Shagass
(19^19 ) pp. l8l-l84) conducted a study to observe the correla
tion between age and heart rate variability. Heart rate variability was determined, in this case, by measuring the heart rate on three beat intervals taken before, during and after pain stimulation (thermal stimulation) and before and after standard questioning. For 12 pain stimulations there were 60 measurements taken. Heart rate variability was then calculated by determining the standard deviation of the 60 measurements. The findings indicate that the heart rate variability decreases with age in a linear fashion. They found no significant correlation between heart rate and heart rate variability. The females' heart rate variability was significantly higher than the males'. The explanation for fhe decrease of heart rate variability with age offered by the authors was the diminishing autonomic nervous system influences with increasing age.
Heart rate variability was said to be ”a superimposi-
(. i on of different sources of variation which are systemized"
(Rohmert , Laurig, Philipp, Luczak, 19731 pp. 33, 38-40) .
Theirs was an attempt to classify, in order of affect on heart rate variability, different categories of internal or external causes of variation. They found high correlations to heart rate variability for muscular work and weak 25 correlations for that of non-muscular ■work. There are many methods of measuring heart rate variability. Their data
■were constructed by examining 50 beat intervals during 500 beats at a steady state heart rate.
The response of the cardiovascular system to non- muscular activities is difficult to interpret and explain.
Kalsbeek (1973, p . 99) discussed sinus arrhythmia and likened it to heart rate irregularity. In his study, he stated that there are 30 different methods for scoring sinus arrhyth mia, and in some cases different scoring methods indicate opposite results for the same data. Firth (1973, p . 7) quoted Kalsbeek as suggesting that instantaneous heart rate can be related to mental load. Within the same article Firth
(1973, pp. 13 and l4) indicated that both heart rate and heart rate variability need further study in order to become useful research tools, and indicated that the cardiovascular re sponse to any stimulus is unpredictable. It is recognized that non-muscular activities can have an effect on the heart rate. However, all non-muscular variations in heart rate are ignored for the purposes of this investigation.
The gross changes in heart rate resulting from sta tic or dynamic muscular loading dominate other physiological and/or psychological causes of variability in heart rate.
Hohmert and his colleagues (1973, p. 43) attest to this fact.
It is for these reasons that this study includes only that variation in heart rate which is induced by muscular activity. 26
Greene, Morris and Viebers (1959, PP* 182 and 183)
described a relationship that may exist between the initial
response to exercise from a resting state and the recovery
t.o a resting state in terms of physiological cost of work.
They plotted metabolic cost over time during response to
exercise and recovery. The plot is similar in form to that
of %RHR over time for the same activity (see Figure 7 ).
There have been no studies which address %RHR as a
measure of metabolic cost. Although, this type of examination
is not within the scope of this study, the analogy of %RHR to metabolic cost was helpful in explaining certain results.
Initial Value of Heart Rate Consideration
In an industrial environment, many times workers are not allowed to complete a task of a certain intensity and then rest or recover before the next task. As is more
often the case, workers move from one physically demanding
task to another without having an opportunity to allow their heart rate to return to a resting steady state. For this reason there can be any number of heart rate patterns for
a task of a certain intensity. A worker's heart rate at the
start of a task would be dependent upon the activity performed
immediately prior to the start of the task. To illustrate the
effeet of the initial value of the heart rate on the heart rate pattern. Figure 8 shows five heart rate patterns which might have all been produced by one individual performing the
same task five times but having five different initial values M
Resting Level Exercise Recovery
Time
Figure 7. Expected area relationship between response and recovery to exercise (solid line). Area A represents oxygen debt and area B represents oxygen payback. 28
i6o
g 130
115
100
Time (seconds)
l'M.u;ure 8. Example HR patterns for varying initial HR values for a task of fixed intensity. 29
of heart rate at the start of the task. For example, heart
rate pattern 2 of Figure 8 increases from 115 %RHR to a
steady state 130 %RHR.
Wilder's (1950, p. 392) Law of Initial Value states that :
. . . the response to agents stimulating the function under investigation depends to a large extent on the initial level of that function. If that level is low there is a tendency to a marked increase; if that value is average this tendency is less marked; if the initial value is high we shall often find minimal or no increase and quite often a paradoxical drop. . . . The exact opposite is true for i inibitory agents.
Wilder intended his law to apply to psychophysical responses to stimuli. It can, however, be applied to cardiac response to muscular activity as well. As the absolute difference be tween the initial and the steady state heart rate required to accomplish the task becomes greater, the more rapid the rate of change of cardiac response. The rate of cardiac response becomes less as heart rate approaches the value required for the task.
Training and Its Effect
Under a controlled environment, the cardiovascular response to a task of a given intensity can be altered con siderably through the effect of training (Brouha, I960, p.
27). Brouha (196O, p. 29) stated his results that the rest ing heart rate decreases with training. The stroke volume also increases with training, thereby allowing the heart to function more effectively by circulating more blood per beat.
Since resting heart rate is effected by training, caution was 30 taken during this investigation to insure that a subject's resting heart rate was not affected by repeated trials during experimentation. The controls are detailed in the procedures section. By utilizing these controls, the effect of training was of no consequence.
Predictive Models for Heart Rate
Dahl and Spence (19?1, PP- 369-376) undertook a study to predict heart rate by task demand characteristics.
Nine questions were asked it out the task. Then each task was rated according to frequency and complexity with 1 (least frequent and complex), 2, or 3 for each question. The tasks which were expected to have the least effect on heart rate increase would have a rating of 9 (sum of 9 ratings of l) and those tasks expected to have the greatest effect on heart rate increase would have a rating of 27 (sum of 9 ratings of
3). Correlations between task demand scale figures and exper imental heart rate were .86 to .90. The above study was not concerned with physical tasks of appreciable intensity. The range of heart rate deviation was small compared to the gross variations in heart rate expected in even light physical work tasks. The heart rates were averaged over all subjects.
Schilpp (19511 pp. k'^h-kk'ÿ) suggested a mathematical description of the heart rate response to exercise. His model was derived from 20 subjects who accomplished the same exercise (36 step-ups on a one foot platform/minute for
2 minutes). The model reflects only an average response and 31
then only for one exercise. He used beats/minute above
resting heart rate for ordinate values. However, he ren
dered no formal definition of resting heart rate. The
exercise performed would be considered heavy exercise at
an expected average heart rate of approximately 200
after two minutes. The exercises for this study required
no more than l60 %RHR for any exercise.
Essentially, Schilpp's model describes only the
transient response of the heart rate pattern. The expected
steady state heart rate is not included in the mathematical
model for any task intensity other than the one previously
described which was for the only exercise investigated. In
order to predict cardiac responses at different levels of work load, it would be necessary to empirically develop a
new set of time constants since steady state is achieved
more quickly for tasks of lesser intensities. Also, it would be necessary to determine how many beats/minute increase
should be attributed to the fast component (A^ below) and how many beats/minute increase should be attributed to the slow component (A^ below).
Schilpp's model has two mathematical components. The first is used to define the heart rate during the first 10 to 15 seconds of exercise, and the second during the remainder of the exercise. The form is as follows: -Kit First component, A^(l-e ) -Kgt Second component, A^Cl-e ) -K.t -Kpt resulting in, Y = A^(l-e ) + A^fl-e ) 32
whore, Y - heart rate at time t
t - time in seconds
= 19 beats/minute
- 61 beats/minute
A -- A +A_ 80 o 1 2 - .385
Kg - .0233.
Both components approach their respective limits of A^ and
A^ over time. Since is much larger than , the first
component approaches its limit (A^) much more rapidly. The
effect of the first component is 90% complete within the
first 7 seconds. The effect of the second component is of
longer duration with half of its effect complete within 30
seconds and 90% complete within 90 seconds. Steady state is
reached at about 4 minutes.
Schilpp indicated that the recovery is not begun
until about 10 seconds after the rest period has begun. It
is interesting to note that other studies (Brouha, Smith,
Delanne, Maxfield, I96O, p. 135) indicated an abrupt decel
eration in heart rate when exercise is stopped. However,
Schilpp admits that "the first 30 seconds of recovery have noI been studied carefully. ..." The recovery formula
was as follows:
-K t. Y - A 'e ^ o where A^' = 76
t ' = tj^-10 (R for recovery) 33
= .0260 .
Note that and are approximately equal indicating that the rate of increase is equivalent to the rate of decrease.
Schilpp's colleague expected a continued steady state heart rate after the start of recovery for about 15 seconds and then rapid drop according to the "fast" component. He then suggested the recovery formula to be
-K t - K t Y = A^e + Age .
After referencing S'hilpp's "description" of the heart rate response to exercise, Suggs (1967, pp. 195-205) used a different approach to develop a model for heart rate response to exercise. He relied heavily on the many studies
(including his own) that indicate oxygen consumption is linearly related to heart rate during both steady state and the transition period after exercise starts or stops.
His model is "based on the more macroscopic physiological responses and will require no explicit reference to specific biochemical changes taking place at the cellular level." In order to develop a model to predict heart rate which can be applicable to industry, a researcher must subscribe to this type of examination. An examination at the cellular level would encompass many generalities and assumptions thereby making it difficult to produce a viable model.
The derivation of Suggs? model will not be discussed in detail here as it is tedious and involved and not directly related to the model for this thesis. Essentially, Suggs 34 used the equation that oxygen intake is equal to external respiration of oxygen plus oxygen consumed to produce body
energy. Using previously developed relationships between
oxygen consumption and heart rate, he transformed the equa tion to include only heart rate as the variable. Then he
empirically established constants for the equation. He developed two equations, one for exercise response and one for recovery. His equations are as follows:
H = heart rate
H = Initial heart rate o H^ = Final heart rate (steady state)
A = H - H e o = .693, for light exercise
Kg = .499, for light exercise
-K^t Exercise H = H - Ae e -Kgt Recovery H = + Ae
Suggs concerned himself with heart rate responses to a step change in exercise level. The model was developed using averaged data from similar trials. Suggs stated that "it is not expected that the results will be useful for predict ing heart rate. ..."
The mechanism that Suggs used to determine an expected steady state heart rate was to convert steady state oxygen consumption to steady state heart rate. He presented a graphic display, complete with data points, but did not 35 supply the regression equation. The regression was deter mined from graphic display to be
H = 60L + 78 e where L = steady state 0^ consumption in liters/minute.
The relationship of 0^ consumption to work load (Sstrand,
1971, p. 352) is
L = . O l W
where ¥ = work load in watts.
By incorporating the above relationships into Suggs' model, steady state heart rate could then be determined and the model could be used to predict heart rate. The above two equations were not presented by Suggs, but are suggested by the author of this thesis to complement the usefulness of
Suggs' model.
Vogt, Meyer-Schwertz, Metz, and Foehr (1973, P* 4$) conducted experiments to extract indirect estimates of muscu lar work stress and environmental heat stress from heart rate variations (heart rate patterns). A product of their experiment was a two part model which could be used to predict heart rate at any period of exercise. Vogt (^;t ad.) stated that as long as other influencing factors are removed, the heart rate depends on mechanical work performed and environ mental heat stress imposed. The experimenters are optimistic about the usefulness of heart rate. They stated;
Even though heart rate itself is not a straight forward measure of cardiac cost, the finding of some precise laws of action and interaction of the factors involved in 36
its combined responses to muscular work and environ mental heat should enhance their value for practical purposes.
They also agree that there is a need to quantify heart rate
patterns.
All (researchers in physiology) agree on the clear cut differences between the respective patterns of initial acceleration and final deceleration of the heart rate. There is, however, no agreement on the quantitative form of the transfer function relating the heart rate "output" to the mechanical power "input" for even the simplest cases of positive (work onset) or negative (work stoppage) transient inputs.
In order to predict heart rate Vogt also detailed the circumstances required. The heart rate must realize a
steady state and to do so the mechanical work (work load) must be submaximal and the work must be performed in the thermal comfort zone. Specifically, the lack of steady state occurs when the mechanical power exceeds the endurance limit, which is defined as "the maximal energy expenditure covered exclusively by aerobic metabolic processes, amount ing to approximately 4 kcal/min (279 watts)." The greatest power requirement for the experiment of this dissertation was 220 watts, which is in the aerobic range. Also, all
experiments were conducted in the thermal comfort zone
(?2°F).
Vogt found two different stages of heart rate vari ation which appeared in sequence for both increases and decreases in mechanical power. The first stage is called the fast variation stage and is of two to five minutes duration. The second stage is the slow variation stage. 37
The former is the concern of this dissertation. Vogt's
model is not an attempt to predict heart rate response to
exercise during the slow variation stage, but is intended to
relate heart rate, heat stress, and •work load over time and
during fixed intensity tasks. Essentially, work load and
standard heart rate at rest are given inputs. Rectal temp
erature and mean skin temperature (taken at four locations)
must be measured dynamically as the task is being performed;
therefore, the model cannot be considered a predictive model
for the slow variation stage. The work load is considered
by translating mechanical power to beats/minute increase
above resting heart rate to a steady state level. The con
version is:
C = b¥
where C = beats/minute above RHR at steady state
b = .4 beats/minute/watt
W = mechanical power in watts.
The heart rate at period j (during the slow variation stage)
is then determined by the following equation:
N. = N + C + 21(T . - 37.0) - 3(A. - 4.00) J O I", J J where = heart rate at period j
N = standard heart rate at rest o T . = rectal temperature at period j ~ , J A ■ = difference (T -T ) between rectal and mean “ J r s skin temperature at period j.
The change in heart rate at period j, during the fast 38 variation stage (concern of this dissertation) is det eriiu.ned by the following equation:
- (Kt-p) D := A(1 - e )
where D = beats per minute change in heart rate
A = steady state value
K = reciprocal of time constant = l/T
t - time measured from instant of step change
of mechanical power
p = pure tir e delay.
The constant K is a function of the initial value of the heart rate and C for heart rate acceleration.
K = -1.35 - .0078 (I + C)
where I - heart rate at the time of the step change
of mechanical power.
For heart rate deceleration
K = -.712 - .0069c.
The heart rate is determined for the fast variation stage by two formulas. For step changes of increasing task inten sity the following equation is applicable:
N . = D + N . J o For step changes of decreasing task intensity the following equation is applicable:
N . = I - D. J In comparison, Schilpp, Suggs and Vogt utilized mathematical equations to predict heart rate patterns.
Schilpp used two exponential components versus one for Suggs 39 and Vogt. The time constants -were set for Schilpp's model, making prediction of light tasks erroneous. Suggs and Vogt allawed for changes in the time constants dependent upon the intensity of the task. Suggs suggested three constants for three general levels of task intensity. The time constants of Vogt's model were a function of resting heart rate and
-work load. Unlike Vogt, neither Schilpp nor Suggs presented a definitive method for deriving the steady state heart rate to be achieved for any given work load. The models of Suggs and Vogt allowed for step increases and decreases in task intensity where Schilpp considered only increase and recovery to a resting state. The models of Schilpp and Vogt required a knowledge of resting heart rate but did not define the mechanism for determining resting heart rate. The models, as presented for all three, made no allowance for variations in sex, physical fitness or any other human variable. The predicted heart rate patterns are assumed to apply to all persons, and, therefore, only one pattern is predicted for each work load and duration for each model. In the results sections a comparison is made of selected heart rate patterns predicted by the three aforementioned mathematical models, the model of this study and the actual observed heart rate patterns. CHAPTER III
THE EXPERIMENT
This chapter is a discussion of the experimental equipment, subjects, and the experimental procedures. It is prefaced by a general description of the experiment and an analysis of the industrial applicability of this technique for heart rate measurement.
General Description of Experiments
There were three experimental testing sessions. The first two, referred to as phase one and two of testing, were conducted for the purpose of quantifying the relationships between work load and steady state %RHR for each subject category and, also, to supply the required empirical data for the predictive model. Phases one and two related to each subject; therefore, it was not necessary to complete phase one for all subjects before beginning phase two. The third testing session, referred to as validation testing, was con ducted for the purpose of evaluating the accuracy and valid ity of the predictive model. During all three experimental testing sessions, subjects were asked to exercise at a con stant rate on a bicycle ergometer for varying task intensi ties while their heart rate response was recorded. Resting
40 kl heart rate was determined at the onset of each testing ses sion.
During phase one, all subjects were screened according to physical fitness. This was accomplished by interviewing each subject. Next, those subjects selected were asked to perform fixed intensity tasks, and the steady state heart rate pattern was recorded. Finally, the sub jects performed tasks which ultimately required a fixed steady state %RHR, In this case, a trial and error tech nique was employed by varying the intensity of the task in order to find the proper work load for each subject.
In order to continue with phase two for a given subject, it was necessary to have completed phase one, since the method of testing in phase two depends on the results of phase one. The subjects performed tasks at the levels of intensity determined in phase one. All tasks resulted in a steady state heart rate but required varying initial values of heart rate.
The validation testing consisted of one subject from each of the four subject categories performing a ser ies of step changes in task intensity (2 or 3 step changes)
The heart rate patterns produced were then compared with the predicted heart rate patterns in order to evaluate the validity of the predictive model. >i2
Industrial Applicability of Experiment
Corlott (1973) states that any technique for tJie mcu'isui'e of heart riiie for industrial use should meet cer tain criteria. These criteria are:
1. acceptable to subject population
2. standardized (give results which may be judged against
defined s t. andar ds )
3- repeatable
4. readily teachable
5. readily interprétable.
Any study concerned with measuring, analyzing, or predicting heart rate should be conducted in a manner such that the above guidelines will be accomplished completely, or if that is not possible, in part.
By discussing each of the above criteria separately, the measurement and consequently the analysis of heart rate data in an industrial environment can be placed into its proper perspective. Fortunately, the state—of—the—art will allow experimenters to monitor and record heart rate via telemetry units with little, if any, inconvenience to the
-subjects. This was shown during a previous study (Pur swell, hr onok, Long, 1972), in which subjects were required to exert themselves beyond that required of the normal indus trial environment. Also, they were required to accomplish movements as quickly as possible. These movements consisted of considerable body movement in almost every possible body attitude. Without exception, the subjects indicated 43
that the monitoring apparatus in no way hindered their
efforts to perform the assigned tasks. It can be assumed,
then, that the heart rate measurements will be acceptable to the subjects in an industrial as well as an experimental
environment.
The predictive model of this study depicts cardiac response in terms of %RHR as well as heart rate. The %RHR
index serves as a common denominator which substantially reduces the interpersonal variations in cardiac responses to exercise. Therefore, oy using %RHR as an index, the results obtained from experimentation and prediction can be
Judged against defined standards.
The results of this study have indicated that heart rate patterns are repeated for individuals accomplishing tasks of similar intensity as long as fatigue does not become a factor. However, fatigue does become a factor under many industrial working conditions. This study was designed to eliminate fatigue as a variable, but it is recognized that a future study should include fatigue as a variable.
The instructions to experimenters for readying a subject in an industrial environment for heart rate mea surements are minimal and should require no more than one to two hours of instruction. In order to obtain predicted heart rate values, the use of a computer is required; how ever, the only knowledge required to run the program is a 44 knowledge of how to complete the input data cards. The analysis of results can again be easily taught to trained personnel working in the area of human factors engineering
since each output will be compared to predefined standards.
Moreover, there should be no interpretation problems since all data and norms will be standardized.
By the preceding logic, the predictive model of this study should be a technique with potential for indus trial use. However, further and broader studies are required to encompass the spectrum of the industrial pop ulation in order to formalize standards and to set work task criteria.
Experimental Apparatus
Description and Use
The only physiological variable measured in this study is that of heart rate. The subject's heart rate was measured over time under varying intensities of physical stress. The range of heart rate investigated was limited to those rates between the lowest steady state heart rate
(RHR) to 160 %RHR (32 to 50 beats/minute above RHR). Most persons can maintain a steady state heart rate of I60 %RHR for short periods of time (1 to 5 minutes). For heart rates much above 160 %RHR, the heart rate increases steadily to exhaustion or maximum attainable heart rate, whichever comes first. It is expected that most industrial tasks will 45
require much less than l60 %RHR on a continuous basis.
In order to collect physiological data •which exhi
bited clearly defined trends, the equipment selected for the
subjects to use was the bicycle ergometer (see Figure 10).
The intensity of the physiological tasks can be increased
or decreased on a continuous scale on the bicycle ergometer.
Similar cranking tasks using the upper limbs result in
noticeable body fatigue after 30 to 60 seconds at heart rates of approximately 120 %RHR. Since tasks requiring a much greater heart rate can be sustained for longer periods of time with less fatigue using the lower limbs, the bicycle
ergometer was selected for this study. As Rstrand (1970, p. 283) indicates, the use of large muscle groups for exer
cise is necessary for tasks which exceed three minutes in order to miniiiiize fatigue.
Recording Instruments
The actual measurement of heart rate was accom plished by equipment manufactured by Narco Bio-Systems, Inc.
The Desk Model Physiograph, DMP-4A, is a strip chart recorder with four recording channels and an event marker. Two chan nels and the event marker were used for monitoring subjects during experiments. The CA-200 and the Type 7O7O channel amplifiers were used in conjunction with the pen motor on the physiograph. The Type 7171 High Gain Coupler was used to receive the heart rate signals from the subjects. The
BT-1200 Diotachometer was utilized to transpose elapsed time 46 for inter-beat intervals to heart rate.
To summarize, the Narco Bio-System components used were as listed below:
1. DMP-4A Desk Model Physiograph
2. CA-200 Channel Amplifier
3. Type 7070 Channel Amplifier
4. Type 7171 High Gain Coupler
5. BT-1200 Biotachometer
Figure 9 illustrates the recording equipment configuration.
Exercise Equipment
The Monark Bicycle Ergometer (Sstrand, 1973) shown in Figure 10 was the exercise equipment used for this exper iment. In order for the subject to exercise in a consistent manner, a speedometer was used so that the subject could accelerate to a reference point (90 rpm). The subject was asked to maintain a certain power output which could be set on the ergometer on a scale graduated in kiloponds (one Kp is the force acting on the mass of one kilogram at normal acceleration of gravity). By maintaining exercise at a set level of energy (kp) over time, power expended can be deter mined. For example, at 50 rpm a reading of 1 kp =
300 kp-meters/minute, and at a two kp setting the power produced is 6OO kp meters/minute, and so on. The unit of power used in this study is watts, where 100 kpm/min =
16.35 watts. 47
Figure 9. Recording Equipment.
Figure 10. Subject exercising on bicycle ergometer. 48
Subjects
The subjects varied in physical fitness and sex.
There -were a total of eight subjects (two in each of four subject categories) tested to collect data for development of the predictive model. There were a total of four subjects
(one in each of four subject categories) tested to collect data to evaluate the model. The total number of subjects was twelve. The subjects were initially selected by somato- type and weight. The somatctyping system used to classify subjects utilizes a combination of endormorphic, mesomorphic and ectomorphic (order of ratings) components to categorize humans. In this system, an individual is assigned a value on a seven-point scale (7 being most characteristic) for the relationship to each of the three forms. This somatotyping system is discussed in detail in Croney's (1971) text on anthropometry. Subjects selected were predominantly meso morphic and had at least a rating of 4 in this category and no more than 3 in the endomorphic and ectomorphic forms.
The weight tolerance was 105 to 120 pounds for females and
145 to l60 pounds for males. The height tolerance was 5'2" to 5'5" for females and 5'9" to 5'11" for males.
Physical Fitness
As an individual improves his physical fitness, he also lowers his resting heart rate (Brouha, I96O, p. 27).
Also, there are fewer beats/minute displacement from resting heart rate under physical stress and the speed of heart rate 49 recovery to a resting state is increased (Bronha, I96O, p. 2?)
Brouha also indicates physical conditioning allows persons to attain "higher levels of performance." Certain physiologi cal changes take place in persons who are committed to train ing and thereby causing the cardiac responses to be different from untrained individuals. There is greater strength in the muscles, improved coordination, and a more developed cardio vascular and respiratory system. All of these changes com bine to aid individuals in accomplishing physical tasks.
General physical training, which results in improved physical fitness, provides an individual with an increased capacity to perform physically demanding tasks of moderate intensity (Brouha, I96O, p. 32). However, for heavier tasks, the person trained specifically for accomplishing a given task will perform it more efficiently than the person with a commensurate amount of general physical training. This study examined individuals of varying states of physical fitness performing tasks of light to moderate intensity. It was expected that those of good physical fitness could accomplish tasks with less expenditure of effort than those whose level of physical fitness was low.
Selecting subjects by physical fitness is a difficult task. Tests of physical fitness are awkward to administer and even more difficult to interpret. The Harvard Step Test which requires a maximal effort on the part of the subject is unreliable as are all tests which require maximal efforts. 50
The experimenter can never fully determine whether the sub
ject was exhausted at termination or just unwilling to exert himself further (5?strand, 1970, p. 350). Any test for physi
cal fitness requiring a maximal effort is susceptible to erroneous results.
A maximal effort was not used for this experiment.
According to data gathered on subjects who exercised to at tain a maximum heart rate, the recovery period to resting heart rate is at least 30 minutes and could be more than one hour (Brouha, I96O, p. 1?). An exercise of this inten sity could cause a considerable oxygen debt and therefore increase the time to full recovery and/or bias results.
Any exercise performed subsequent to execution of a maximal effort would be effected. A maximal effort for sedentary persons could delay testing for days and could possibly be harmful to their health. It should also be noted that tasks requiring a maximal effort are seldom found in industry.
As for sub-maximal work test to measure physical fitness, Sstrand (1970, pp. 358-359) states that there are two situations in which they can be used. First, they can be used in clinical examinations in order to examine the cardiovascular system under functional stress. And second, they can be used to evaluate the effectiveness of a training program. In the first situation the test is for reliability of the cardiovascular system, and in the second situation the test is used to examine relative changes in an individual's heart rate. In neither situation can an experimenter draw 51
conclusions about an individual's level of physical fitness.
For the above reasons subjects were selected and
placed in one of two levels of physical fitness according
to a five point classification scheme for state of training
or physical fitness suggested by Sstrand (1973, p . 32).
Sstrand's five level classification system is as follows:
1. Completely untrained
2. Sporadic muscular activity--a few times per month
3. Regular but light exercise--once to twice per month
4. Rather intensive training one or more times per week
5. Hard training for competition several times per week.
There are only two levels of physical fitness for this study,
In order to assure a definite distinction between these two levels, persons of level three above were not accepted as subjects. An extensive interview was conducted with each subject in order to determine if they could be classified in levels one, two, four or five above (see Appendix 2 for a brief description of each subject's state of physical fit ness and exercise frequency). If a subject was of level one or two then he was classified as being sedentary (S).
If a subject was of level four or five he was classified as being of good physical fitness (G).
Sex
The other subject variable was sex, male (M) and female (F ). The subject categories are as shown in Table
1. Appendix 2 contains a descriptive summary of subjects tested for this study. 52
TABLE 1
SUBJECTCATEGORIES
Male F emale
Good Physical Fitness MG FG
Sedentary MS FS 53
Experimental Procedures
Controls
Env ir onm ent a1
All testing tvas accomplished in a controlled environ ment with a temperature of ?2°F + 2° and a relative humidity
of 4$% + These conditions were held constant so that
temperature and humidity would not be factors. The time of testing was from 10:00 hours to l6:00 hours. The considera ble time span was necessary because of the length of each
experimental session per subject. The time of day had little noticeable effect on the heart rate patterns or the resting heart rate since this experiment was focused on gross changes not often realized in time-of-day changes in physiological processes.
Subject
Subjects were asked in advance to adhere strictly to good eating (three well-balanced meals/day) and sleeping practices (approximately eight hours/day) for three days prior to testing. The nutritional problem of one's diet is of importance and must be considered. A quantity defi
ciency could result in a caloric consumption that is less
than adequate for the work to be accomplished and thereby result in a reduced efficiency of the worker (Brouha, i960, p. 25). Qualitatively, Vitamin A and Vitamin D are not essential for producing physical work, but Vitamin C has 54 beoii sliown helpful to those working under heat stress.
Another study proved that Vitamin B is imperative for good
physical efficiency. Brouha (196O, p. 25) cites Wald, John
son, and Weaver to state these reactions to Vitamin A, B, C,
and D. Consequently, certain nutritional imbalances could
cause a physical inefficiency. Insufficient rest could also
result in physical inefficiencies.
Caution was taken to insure that the subject's per
formance was not affected by training. Subjects were tested
on two days only. The testing sessions were one week apart
and no exercise was in excess of 240 seconds. The subjects
exercised no more than 10% of the time thereby allowing 90%
of the testing time for rest and recovery. No exercise was
so intense as to require a maximal effort, or even close to
it.
Testing Procedures
The actual testing sessions for phases one and two were scheduled on two separate days and one week apart for
each individual. It was necessary to schedule rest periods between trials so as to eliminate an overall fatigue effect. Although the tasks were of varying intensities, the subjects were required to maintains resting heart rate
for five minutes prior to each trial, thereby making the minimum rest period between each exercise at least five minutes.
As the subjects arrived at the testing center, each 55
was prepared by the experimenter for recording of heart
beats. There are several methods for placing surface elec
trodes on subjects, but the only acceptable method for subjects
engaged in exercise is a chest cluster. In any other arrange
ments, to include limbs, noise is generated in the signal by
the muscles in the limbs.
Phase One of Testing
The subject, although interviewed briefly prior to
the testing session, was again interviewed to assure proper
placement in the appropriate subject category. If the sub
ject did not fit into the subject categories of this study,
then experimentation was discontinued and another subject
was engaged. In order to acclimatize the subject to the
experimental environment and to the bicycle ergometer, the
bicycle ergometer was adjusted to adhere to the subject's
arthropometric dimensions, and then the subject was allowed
to exercise at will. Once the subject felt familiar with
the bicycle ergometer, he was then asked to practice main
taining 50 rpm. The subject was then seated for fifteen
minutes. His resting heart rate was then recorded for five minutes. The average resting heart rate was determined by
counting the number of heart beats in this five minute period
to determine the average beats per minute at rest (RHR).
In order to determine the work load to steady state
%RHR relationship, each subject performed three tasks of which
one was of light intensity, one of moderately heavy intensity, 56
and the intensity of the third task was approximately midway
between that of the former and the latter tasks. All tasks were performed on the bicycle ergometer until a steady state
heart rate was attained. This first task was of sufficient
intensity to raise the heart rate of the subject from 8 to
15 beats/minute above resting heart rate. The second task required an increase in heart rate of 15 to 25 beats/minute.
The third task required an increase in heart rate from 25 to
40 beats/minute. In each case steady state was maintained
for 30 seconds. The experimenter was then able to proceed
to part two of phase one with an idea of the steady state heart rate to work load relationship for each subject.
The purpose of the second part of phase one of test
ing was to determine the work loads required for a particu lar subject's heart rate to steady state at %RHR levels of
120 %RHR, l4o %RHR and 16O %RHR. Conversion tables for translating heart rate to %RHR and %RHR to heart rate aided the experimenter in dealing with the two measures of cardiac response. (Conversion tables shown, in part, in Appendix l4).
The testing included a trial and error technique. The experi menter could estimate the required work load from the results of part one. The experimenter set the bicycle ergometer at the work load level that he thought might require a steady state of 120 %RHR and asked the subject to exercise. If the steady state heart rate was not within i 2% of 120 %RHR, fine adjustments in work load were made by the experimenter, and the above procedure was repeated until the subject's 57
heart rate pattern v?as repeatable to a predetermined 120 %RHR.
This was accomplished for the three levels of %RHR and phase
one was then completed and the subject was scheduled to
return one week later for phase two.
Phase one instructions to subjects are presented in
Appendix 1.
Phase Two of Testing
The second phase was conducted one week after the
completion of the first ph. se. The objective was to examine
each subject's response to all combinations of step changes
in task intensities of exercise for 100 %RHR, 120 %RHR,
l40 %RIfR and l60 %R1IR. That is, the initial value could be
any of the four levels of %RHR and the task could require
a steady state %RHR at any of the four levels of %RHR. The
step task matrix is shown in Table 2.
After the subject had been prepared by the experi menter for recording of heart rate, he was asked to accom
plish a few lighL tasks which required an increase of fifteen
to thirty beats/minute in heart rate. This exercise was
intended to acclimatize the subject to the experimental
environment. The subject's resting heart rate was recorded
in the manner described in phase one. If the subject's resting heart rate was not within i 2 beats/minute of that resting heart rate recorded for phase one, testing was post poned until a later date. The experiment proceeded to include all tasks noted in Table 2 for each subject. The intensity 58
TABLE 2
MATRIX OF EXPERIMENTAL STEP CHANGES IN TASK INTENSITY
Initial Steady State Value of %RHR Value of 9oRHR 160 140 120 100
160 - D' C A'
140 D - B ' E'
120 C B - F'
100 A E F - 59
of each task was preset according to data gathered in phase
one of testing.
The tasks represented by the cells in Table 2 were
combined in pairs in order to expedite test procedures. The
tasks were completed for each continuous exercise on the
bicycle ergometer. For example, Task B and B ' were completed
during one continuous exercise on the bicycle ergometer. The
task intensity was set at the onset of the exercise such chat
the subject would realize a steady state of 120 %RHR. This
was the initial value (IV) for task B. The intensity was
then adjusted such that the subject would realize a steady
state of l40 %RHE. After a 50 second steady state period
the task intensity was adjusted such that the subject would realize a steady state of 120 %RHR. Thus, l40 /^RHR was the
initial value for task B '. All tasks denoted by a prime
(e.g., A') are recovery states. That is, the task is of
lesser intensity than the preceding task. There were six
trials (a trial being one continuous exercise) which each
subject performed. The exercises were AA', BB', C C , DD',
EE' and FF'. Once these experiments had been performed and
the data recorded for all eight subjects twice, the testing required to furnish hard data (empirically derived data)
for the predictive model was complete.
Phase two instructions to subjects are presented in
Appendix 1. 6o
Validation Testing
In order to validate the experiment, four subjects
■were selected such that each of the four subject categories
■were represented. Subjects used in phases one and two for for data development were not included. Each subject per formed six series of tasks. A series is defined as a combi nation of adjacent step changes in task intensity. The dur ation of each series was 240 seconds and each series con sisted of either 2 or 3 step changes in task intensity.
The subject was at rest at the start of each series.
The step changes in task intensities and associated durations were selected at random for each series for one subject category. Then the step changes for the series of the other three subject categories were chosen such that all like series would require approximately the same steady state %RHRs for all subject categories. That is, the pre dicted heart rate patterns for series one would be approxi mately the same in terms of %R H R , and those for series two would be approximately the same, and so on. This procedure was followed so that there would be a similarity in the cardiac response for each series between subject categories; therefore, the subject category responses could be compared in terms of %RHR.
All series (step changes and durations) for all subject categories are presented in Chapter V.
The subject was introduced to the bicycle ergometer 61
and his resting heart rate was determined according to the
procedures detailed in phase one. Each subject was given
a twenty minute rest period prior to each of the six series
of step changes. The subject's heart rate was recorded
throughout each series. The step changes in task intensity
and durations, subject category, and resting heart rate were input into the predictive model. Utilizing the pre
dictive model, the heart rate responses were predicted and
then compared to the observed heart rate responses in order
to evaluate the validity of the model.
Instructions to subjects for the validation testing are presented in Appendix 1.
Collection of Heart Rate Data from Recorded Output
The individual heart beats and the heart rate based
on the inter-beat interval were recorded continuously on the strip chart recorder during rest and exercise.
The heart beat data were necessary for determining
the resting heart rate as described in phase one of testing.
The heart rate data were used to determine the empirically derived hard data patterns of 20 %RHR step changes used in
the predictive model and to evaluate the predictive model.
Figure 11 presents an actual recorded response of a sedentary female while performing tasks AA' (lOO to l6o to 100 %RHR). From the calibrated output of the strip chart recorder, the data were transferred to Form 3 (see
Appendix 6) at 10 second intervals in discrete heart 62
PH 4-Channel R/L Part N o . 713-0004
Sedentary Female Task AA
S3,160ZRHR, heart rate
150 Watt no load' exercise recovery RHR RHR
sec
heart beats
O NARCO UIO-SYSU'MS inc HoustON.T e x a s U.5.A.
Figure 11. Strip chart recorder output during "exercise AA' for sedentary female. 63 rate values. In some cases, equipment artifacts caused discontinuities in the recorded heart rate patterns. In these cases the closest, most representative point was selected as the data point transferred to Form 3- After the data had been collected in discrete heart rate values, the conversion tables (shown, in part, in Appendix l4) were used to transform all heart rate data to %RHR. These data were recorded on Form 2 of Appendix 6.
The heart rate data for validation testing were taken directly from the calibrated strip chart recorder output at 10 second intervals. It was not necessary to convert the heart rate data to %RHR since the predictive model was evaluated in terms of heart rate. CHAPTER IV
THE EXPERIMENTAL DESIGN AND PREDICTIVE MODEL
The contents of this chapter include a discussion of the experimental design which was used for the collection and evaluation of the heart rate data necessary for the develop ment of the predictive model. Also, the methodology of the predictive model is presented in detail. A numeric example is used to illustrate the logic and computational procedures of the predictive model.
The Experimental Design for Data Collection
The experimental design of this study was not estab lished to evaluate the results of the model but rather to form a basis by which to collect and evaluate the data (hard data patterns) which constitute the foundation of the pre dictive model.
The main effects of sex and physical fitness were discussed in detail in the preceding chapter. There are two levels of sex, male and female. There are two levels of physical fitness, good and sedentary. Consequently, there are four subject categories.
64 65
The other main effects are time and subjects. The
data (heart rate) for each heart rate pattern were collected
at ten second intervals at time 0, 10, 20, etc. (nine levels
of time). The ten second interval provides a reasonable
balance between the sensitivity of the data and elapsed time.
There were a total of eight subjects tested to supply empiri
cal data for the predictive model (two subjects from each of the
four subject categories). There was one replication for each
trial; consequently, there are four data points for each
time period for each hard data pattern for each subject cate
gory.
The experimental design is for a nested-factorial
experiment with the main effects of sex, physical fitness,
time periods and subjects. The subject factor is nested under sex and physical fitness. This analysis of variance model is applicable for investigating one heart rate pattern
(e.g., 100 to l40 %RHR). There are twelve step changes in all and therefore twelve ANOVAs. The ANOVAs serve a two fold purpose in that the results indicate the significance of the main effects and as a by-product, the cell means by time period and by subject category provide the hard data patterns
for the predictive model.
In t]ie analysis of variance model, sex is denoted by
"S," physical fitness by "P," subjects by "V," and time periods by "T." Levels 1 and 2 of sex are male and female, respectively. Levels 1 and 2 of physical fitness are good 66 physical fitness and sedentary, respectively. Each level for subjects represents one subject. Levels 1 through 9 of the time periods are 0, 10, 20, through 80 seconds, respectively. The mathematical model is a mixed model.
hjklm = " " \ " h " SPjk + ST,^ . * Vi(jk)
^ ^ ^ ^jkl " ^^il(jk) ®m(ijkl) ■where , a = grand mean
- subjects i - 1,2, ..., 8
Sj - sex j = 1,2
^k " physical fitness k = 1,2
- time period 1 = 1,2, ..., 9 e = experimental error m = 1,2. m ^ Table 3 shows the sources of variation and associated degrees of freedom as well as the appropriate denominator for the K-Hal:io for testing the significance of the associ ated main effect or interaction. Table 4 shows the experi mental design.
The Predictive Model
Introduction The predictive model of this study, referred to as the predictive model, was conceived and developed to make allowances for variations in an individual's state of physi cal fitness, sex and resting heart rate. This prediction process is accomplished by extrapolating cardiac responses to exercise from empirically derived heart rate patterns, referred to as hard data patterns, for various subject categories. 67
TABLE 3
SOURCES OF VARIATION, ASSOCIATED DEGREES OF FREEDOM, AND DENOMINATOR OF F-RATIO FOR ANOVA
Source of Degrees of Denominator Variation Freedom of F-Ratio
U 1
S - sex 1 V
P - physical fitness 1 V
T - time 8 VT
SP 1 V
ST 8 VT
PT 8 VT
V - subjects 4
SPT 8 VT
VT 32
Error _Z2 l44 68
TABLE k
FORMAT OF BATA COLLECTION SCHEME
Sex Time Male F emale Periods Pbysical Fitness Physical Fitness (sec) Sedentary Good Sedentary Good Subject - 1 2 3 4 5 6 7 8
0
10
20
30
4o
50
60
70
8o 69
This approach differs from that of previous models in that previously, allowances were made only for resting heart rate and all previous models were stated in terms of mathe matical equations. By categorizing subjects into two lev els of physical fitness and sex, between subject variations in heart rate response to exercise can be reduced consid erably by using percent of resting heart rate (%RHR) as a base. The rationale for this approach was predicated on four basic assumptions. First, individuals of a particu lar category adhere to a linear relationship between work load and steady state %RHR. Second, the heart rate pat terns produced for any given work load by individuals of the same subject category are similar in form when presented as a function of %RHR. Third, heart rate patterns for any step change in work load can be extrapolated from hard data patterns, and these patterns can be shifted along the
"time" axis. Fourth, it is reasonable that the individu al's resting heart rate is relatively stable from year to year, except for instances when the individual changes his exercise habits.
Hard Data Patterns
Empirical data were collected for each subject cate gory according to the experimental procedures set forth in the preceding chapter. The empirical data which are values of "«RHR at 10 second intervals, are the basis for the hard data patterns of l8o seconds duration to include all possible 70
combinations of step changes of task intensity for 100 %RHR,
120 %R11R, l40 %RHR, and l60 %RHR. There are sixteen
in all for each subject category. Twelve were derived
through experimentation, and the other four are steady state
with no change in task intensity (e.g., 120 ?^RHR to 120 %RHR,
140 %RHR to 140 %RHR).
The hard data patterns were coded for future refer
ence. The coded symbols are two character designators where
the first character is alphabetic and the second numeric.
The alphabetic character refers to the initial value of the pattern, where:
A is 100 %RHR. B is 120 %RHR. C is 140 %RHR. D is 160 %RHR.
The numeric character refers to the steady state value of the
pattern, where:
1 is 100 %RHR. 2 is 120 %RHR. 3 is 140 %RHR. 4 is 160 %RHR.
Table 5 presents a list of hard data patterns and the asso
ciated symbols.
The hard data patterns are presented by subject cate
gory in Appendix 3. Each data point is the result of an
average of four instantaneous heart rate values at time t.
The average was a result of two trials each for two subjects.
Other experimenters (Vogt, 1973; Schilpp, 1951; Suggs,
1967) have presented heart rate patterns as either monotically 71
TABLE 5
NOMENCLATURE FOR HARD DATA PATTERNS
Initial St eady Symbol Value State (%RHR) (°/oRHR)
Al 100 100 A2 100 120 A3 100 140 A 4 100 160
B1 120 100 B2 120 120 B3 120 i4o B4 120 l6o
Cl 140 100 C2 140 120 C3 l40 140 C4 140 l6o
D1 160 100 D2 160 120 D3 i6o 140 d 4 l6o l6o 72
increasing or decreasing depending on the direction of the
step change of task intensity. The predicted results of
previous models were not consistent with the hard data pat
terns of this study. Patterns produced by these models do not exhibit points of inflection or linear trends for any step change in task intensity. However, both points of
inflection and linear trends were found during the data
collection phase of this experiment. The points of inflec
tion during the transient responses were expected since
there is a lag in cardiac response to any step change
in task intensity. Well defined linear trends were found in patterns produced by the sedentary groups. Only one point
of inflection was allowed in a hard data pattern. For the
time period after the point of inflection, it was expected
that the patterns increased and decreased at a zero or
decreasing rate. To obtain this feature, it was necessary
to smooth several data points to assure only one point of inflection. Only 30 of 1152 (less than 3%) hard data points were adjusted and then by no more than 2 %RHR. No one heart rate pattern required an adjustment for more than two data points. The method used to adjust data points was straight forward. Any point of inflection for either increasing or decreasing heart rate patterns was adjusted up or down such
that the slope relative to the two adjacent data points was
either zero or decreasing. It was not necessary to adjust any data points in the time period just prior to the point of inflection.
Figures 24 through 35 on pages 115 through 120 dis play the hard data patterns for all subject categories and 73 the overall average.
The relationship between power and steady state
%RHR for each subject group was determined to be linear for each subject category. These relationships served as the basis for determining at what level of work a particular subject's heart rate could be expected to reach a specified steady state level. Figure 15 on page 96 of Chapter V illustrates the relative slopes and intercepts of each of the regression equations. These are discussed further in the results section.
General Discussion of Methodology
This section is a general discussion of the methodo logy that is used by the predictive model. The following section presents a numeric illustration with an example of inputs, calculations, and outputs.
Required Input
The input required in order to predict an individu al's cardiac response to a series of fixed intensity tasks can be obtained easily by an interview and by measuring one physiological variable. An interview is necessary to deter mine the subject's state of physical fitness (good or seden tary) and the resting heart rate can be obtained by using the procedures set forth in the experimental procedures section. Other inputs include the duration and intensity of each of the tasks and the number of tasks. There can be either two or three adjacent tasks with an accumulative duration of no more than 240 seconds. If the initial value 74 of the heart rate at work onset is other than resting heart rate, the initial value, in %RHR, is an input. This enables the prediction of heart rate responses for an ongoing exer cise. To summarize the input required for predicting the cardiac response to a series of tasks, the following is required :
1. Subject category (MG, MS, FG, FS),
2. Resting heart rate (beats/minute),
3. Number of tasks (2 or 3),
4. Initial value of heart rate as %RHR (100 if resting at
work onset),
5. Work load (in watts) and duration (in seconds) of each
task.
Derivation of Step Change in %RHR
In order to predict a heart rate pattern, it is necessary to determine the expected step change in %RHR.
The initial value is either given at work onset or is the value at the time of the step change. The expected steady state %RHR is then derived from the linear relationship of work load to steady state %RHR for the appropriate subject category. (See Figure 15 on page 9 6 .) The initial value and the expected steady state %RHR depict the direction and magnitude of the step change in %RHR. For example, given an initial value of 100 %RHR and an expected steady state
/oRlIR of l40 %RHR, the expected cardiac response is an increasing step change of 40 %RHR.
Selection of Appropriate Hard Data Patterns
It is apparent that a heart rate pattern for a 75 step change of 100 to 130 %RHR is not available in the hard data patterns. However, this pattern can be accurately extrapolated from the hard data patterns which form the core of the predictive model. Given any step change in task intensity for any subject category, the step change in %RHR can be derived, thereby yielding the initial value and the steady state %RHR, 100 and 130 %RHR, respectively, in the above example. For each heart rate pattern to be predicted
(P) the predictive model requires two hard data patterns which encompass P. The initial value of P is numerically within or equal to the initial value of the two hard data patterns (e.g., 100 %RHR 5 IV < 120 %RHR). The steady state %RHR of P is within or equal to the steady state
%RHR (SS) values of the hard data patterns (e.g., 120 %RHR
^ SS < l40 %RHR). These hard data patterns which encompass
P will hereafter be referred to as high and low patterns.
The high (H) and low (L) patterns are selected such that the absolute difference, j j is no greater than 20 %RHR at time t equal zero and at times when both patterns are at steady state. This means that there can be a difference of no more than 10 %RHR between P and H, or between P and L at IV and SS. The initial value (I V ) of
P will be within one of the three following limits:
100 %RHR 5 IV < 120 %RHR, or 120 %RHR 5 IV < l40 %RHR, or 140 %RHR < IV g l60 %RHR.
The steady state (SS) of P will be within one of the three following limits: 76
100 '/oRHR g SS < 120 %RHR, or 120 %RHR S SS < l40 %RHR, or 140 %RHR < SS S l60 %RHR.
Therefore, P can be within any combination shown in Table 6 .
As noted in the table, a decreasing step change from an IV of more than l40 %RHR for the sedentary subject categories is not included in the predictive model. (This omission is explained in detail in the results section of Chapter V.)
Tlierefore, the decreasing step changes for combination
(9) and combination (8) are permitted for subject categories of good physical fitness only.
The low and high patterns are unique for combina tions (2 ), (3 ), and (6) of Table 6 , (increasing) and for combination (8) (decreasing). However, for combinations
(1 ), (5 ), and (9 ), P can either be increasing or decreasing since the initial value and steady state %RHR intervals are the same. Therefore, each of these combinations has a pair of low and high patterns. The selection of the appropriate low and high patterns are dependent upon the IV to SS rela tionship. There is also a pair of low and high patterns for combinations (4) and (7 ) of Table 6 . For combinations 4) and 7), if the decrease is to a resting state (to 100 %RHR), both the high and the low patterns decrease to a resting state.
Otherwise, only the low decreases to a resting state.
There are sixteen hard data patterns of I80 seconds duration which contain 19 data points each at 10 second intervals for each of the four subject categories. Appendix 77
TABLE 6
COMBINATIONS OF POSSIBLE STEP CHANGES IN %RHR FOR P
Initial Value Steady State %RHR ICO to 120 120 to l40 l40 to i6o %RHR %RHR %RHR
100 to 120 "/oRHR (1) (4) (7)^
120 to l40 %RHR (2) (5) (8)2 l40 to l60 %RHR (3) (6) (9)3
^To RHR only, for S o “For G only 3 Increase only, for S 78
3 contains all hard data patterns. Figure 12 presents a
flowchart of the decision process for selection of the high
and low patterns.
The Predicted Heart Rate Pattern Not Adjusted for Time
After the appropriate high and low patterns are
selected, a heart rate pattern with the same steady state
%RHR (SS) of the pattern to be predicted can be extrapolated
from the high and the low. This is accomplished by linear
interpolation. The ratio Tl) is derived from the following
equation:
_ SS - LSS - HSS - LSS
where :
LSS = steady state of the low pattern
HSS = steady state of the high pattern
This ratio is multiplied times the difference of the high and
the low patterns at time t (for 10 second intervals). The
results are then added at the appropriate time period to the
low heart rate pattern. The predicted heart rate pattern
not adjusted for time (Z) is derived by the following equa
tion:
Zt = - q ) R i + q
where :
= point on P not adjusted for time at time t
H, = point on H at time t t L^ = point on L at time t C 79
N - No Y = Yes L = Low Pattern H = High Pattern p - Physical Fitness G - Good Al, A2, «.., D4 = Hard Data Patterns 1 ), 2), ..., 9 ) = IV < SS Combinations (See H4— A2 < D Table 6 ) IV = Initial Value SS = Steady State %RHR
Le-^1 H<— B2 \/ ■>( H<— C2 0 N
Y . Lt^Bl H < ^ 1 A0
L*— Cl Y V H<— D1 —A0
>—Ï ^ -, L< Cl \( H*— D2 A0
Figure 12. Selection process for high and low heart rate patterns. 80
IV < SS
ïj^— C2 H<— C3
L<— Cl
Error
>/
Figure 12. Continued. 8 l
Error <3
I/— 03 s( H"»— 04 A
Error O
^Continue ^ ©
\j/ ^ Stop ^
Figure 12. Continued. 82
t ^ 0 , 1 0 , 2 0 , ..., iBo.
Silice the initial value of Z may or may not be equivalent to
that of P, Z is said to be not adjusted for time. Z can be
shifted along the time axis such that the intercept will be
equivalent to the IV of P.
There are tivo circumstances in which P can be calcu
lated directly without having to adjust for time. This
occurs for combinations (4) and (7) of Table 6, when the
step change is to a resting state.In these cases, both the high and the low patterns decrease to a resting state or to
100 %RIIR; therefore, the ratio used to calculate P directly
is derived from IV as follows:
IV - L R3 = H - L o o where :
L = value of low pattern at time zero o = value of high pattern at time zero.
Pattern P is then derived as follows:
h = <«t - + h -
All other combinations must be adjusted for time as discussed
in the following section.
The Predicted Heart Rate Pattern Adjusted for Time
The steady state of pattern Z is the same as that of
Pattern P; however, the initial value of Z (Z^) is dependent upon R1 and may or may not be equivalent to IV. In order to 83 derive a heart rate pattern with the required IV and SS, it is then necessary to adjust Z by shifting Z along the time axis to a point where the intercept with the y axis
(time = O) is equal to IV. This heart rate pattern is adjusted for time and is equivalent to P.
The direction of the shift of Z along the time axis to derive P is dependent on the relation of IV to Z^.
If Z^ is greater than IV then Z is shifted to the right.
If Z is less than IV then Z is shifted to the left. If o Z is equal to IV then Z is equal to P. To summarize. o ^ If Z > t t + T o IV, Z < t <' ' t — T o IV, Z = z = P o IV, where :
T = shift in time (seconds).
In order to determine T, the amount of shift in time, the 10 second interval of 2 in which IV is contained must be determined (Z^ S IV < Since the data points of Z are at 10 second intervals, it is likely that the IV will not be equal to some Z^. Having selected the appropriate 10 second interval in Z (Z to Z , «), it is a a + 10 then necessary to determine the ratio of the difference between IV and Z and the difference between Z _. and Z . a a +10 a The resultant ratio, R2, is shown below. 84 IIV - z R ______2 - l^a.lO-^a
The ratio R2 is then multiplied times each interval differ ence, ^t"’^t4lo| ’ the result is either added to or sub tracted from , depending on whether the heart rate is increasing or decreasing during the interval. The resultant heart rate pattern is P. The calculation is performed accord ing to the following equation:
- %t| ) - ^ 2 Add, if ^
Subtract, if ^ ^t*
The net effect of the above transformation is to shift Z to the right (l-R2 )lO seconds or to the left R2(l0+a) seconds; therefore,
= ^t-(l-R2)lO shifts to right, or P, Z, noCTrv \ for shifts to left, t t+R2(10+a)
It can be noted that when Z is shifted to the right, that a time interval of "negative time" is involved. It is therefore necessary to project the high and the low patterns through the time interval of -10 to 0 seconds. This is accomplished by including a point on L and H at time -10.
These extra points are not extrapolated from the hard data patterns. This would induce considerable error and is not necessary since the only reason for the negative time requirement is to determine the ratio R2 when Z is shifted to t?ic left. In order that only one data point be included. 85
it is assumed that if the low and high patterns were extra
polated to negative time, they would be approximately 20
%RHR apart at time -10 or be parallel projections. The
data indicate that this assumption is well founded. Since
they are parallel, the included data points can be fixed
such that the range of %RHR for the interval (20 %RHR) is
included in the 10 second interval from -10 to 0 seconds.
For increasing L and H, the data points at time -10 are 20
/-oRHR lower than L and H . For decreasing L and H, the pro- o o jacted points become 20 %RHR higher than and . For steady
state L and H, the projected points become the steady state
value.
The predicted heart rate pattern P is in terms of
%RHR. It is a simple procedure to translate P to a heart
rate pattern which predicts the absolute heart rate (H).
This is accomplished by the following equation:
= (P^ X RHR)/100
where :
RHR = resting heart rate.
Predicting Heart Rate Patterns for a Series of Fixed Intensity Tasks
The predictive model will accommodate a series of up
to three tasks with a combined duration of no more than four
minutes. The predicted heart rate pattern for each task is
derived according to the procedures presented in the preced
ing sections. Each heart rate pattern predicted for each 86 task j s of 3 iiiinutos duration; however, only that portion of pattern which is called for in the input specifications is utilized (e.g., $0 watts for 100 seconds). The model pre dicts the pattern for task number one first, task number two second and so on. The final %RHR predicted for task number one becomes the initial value for task number two, and so on. In the example above, P,of task number one becomes P JLUU O of task number two. It is in this manner that a series of heart rate patterns can be linked together.
A Numeric Example of the Predictive Model
The following discussion is a numeric example of the method by which the predictive model predicts the cardiac response to a series of tasks. The following information is
given:
Sex Female Physical fitness Sedentary Resting heart rate 80 beats/minute Initial value 100 %RHR Number of tasks 3 Task number 1 work load 60 watts duration 70 seconds task number 2 work load 100 watts duration 70 seconds task number 3 work load 0 watts (rest) duration 100 seconds
It is not necessary to perform all calculations for
all tasks in order to illustrate the basic procedures fol
lowed by the model in predicting heart rate patterns. The
patterns for task two and three are presented in the follow
ing example. The prediction of pattern two illustrates the
basic predictive technique for all step changes in task 87
intensity and, also, most clearly illustrates the linking of
the three patterns. The prediction of pattern three illus
trates the specific predictive technique used for predicting
patterns for recovery to a resting state. Assume that the
heart rate pattern for task number one has already been
predicted and is known. The steady state %RHR (SS) is 129
%RHR at an elapsed time of 50 seconds and, therefore, time
equal to 70 seconds, the time at which the task intensity
is changed to 100 watts. The initial value (IV) for the 100 watt task (task number two; then becomes 129 %RHR.
The steady state %RHR is determined from the appro
priate empirically derived work load to steady state %RHR relationship. For sedentary females:
SS = .451W + 103 where :
SS = expected steady state %RHR
W = work load in watts.
At 100 watts, SS becomes l46 %RHR. The step change in %RHR
is then expected to be 129 %RHR to l46 %RHR.
After having determined the step change in cardiac response, the high and low hard data patterns are selected
from the sixteen hard data patterns of the sedentary female
subject category. The details of the selection procedure were presented in the preceding section in Figure 1 2 . In this example, the initial value is between 120 and l40 %RHR and the steady state value is between l40 and l60 %RHR. 88
Those limits for IV and SS require the hard data patterns of B3 (120 to l40 %RHR) for the low pattern and C4 (l40 to
160 /oFdIR) for the high pattern. The data for these patterns arc presented in Appendix 3. Figure 13 is a plot of the high and low patterns.
The pattern not adjusted for time, Z, is then derived from the high and the low patterns. It is known that the SS is expected to be l46 %RHR. The high and low steady states are I60 and l40 respectively. The ratio R1 can be computed.
„ 146 - l40 _ _ 1 " 160 - 140 "
Z can then be computed.
= (140-120).3 + 120 = 126
= (152-132).3 + 132 = 138
ZgQ = (157-137).3 + 137 = 143
Z = (i 6o - i 4o ).3 + 140 = l46
^40’^50’'•*’^180 ^ steady state l46 Z is shown in Figure 13. It can be observed that the initial value of pattern Z is 125 %RHR. The desired initial value is 129 /oRIlR. The pattern Z must be shifted to the left and adjusted for time such that the intercept is 129 %RHR.
Since Z^ is less than IV, Z is shifted to the left to intercept at 129 %RHR. The interval of Z(Z^ to Z^+lO^ which IV is contained is then determined in order to deter mine the magnitude of the shift. In the example,
Zo < IV A A 0 0 O = Z (pattern not adjusted \D for time) ^ = P (pattern to be predicted) = high and low patterns = each arrow originates 110. from a line connecting 20 40 adjacent points of Z. Time The length of the arrows denotes the time shift required so that Z inter cepts at IV = 129. The 100 shift of Z results in P. I 1 " "~T“ 10 20 30 40 50 60 70 8o T i me (sec) Figure 13 Graphic example of derivation of predicted heart rate pattern. Inset shows lateral shift of Z to intercept at IV = 129, thereby becoming P. 90 126 s 129 < 1 3 8 . Based on the above interval R2 is computed. = ilB-r-ill- = *25 P is then computed as follows: P = 126 + (138-126).25 = 129 P^Q = 137 + (143-138). 25 = 138 P^Q = 143 + (146-143).25 = 144 P_Q = l46 + (146-146).25 = l46 ^40’^50’■ ’ ■’^180 steady state l46 The arrows on Figure 13 indicate the direction and magnitude of the shift of Z. The magnitude for a shift to the left is .2 5 (10+0 ) seconds (2.5 seconds). Since the series of tasks is ongoing, thepredicted heart rate pattern must be placed in the appropriate time period. Task number one is of 70 seconds duration with task number two beginning at time 70. Therefore, P^ is at time 7 0 , P^Q at 80 and so on, until the duration of task two has elapsed at time 150. After I 50 seconds the work load becomes zero (task number three) and the cardiac response to recovery is then predicted. The initial value is l46 %RHR and the expected steady state is 100 %RHR. Since the step change indicates combination (7) of Table 6 and, also, the step change is to a resting state, both the high and low patterns are patterns which decrease to 100 'oRHR. It can be observed from Figure l4 that the low and high patterns are hard data patterns Ci(l40 to 100 %RHR) A 160 «' 150 ■ A / \ = P (pattern to be A predicted) l40 ® = high and low pat- t em s A 130 A « 120 . A 110 ' A A 100 / A 10 20 30 40 50 - 60 . 70 80 90 T i m e (sec) Figure l 4 . Graphic example of derivation of predicted heart rate pattern for recovery to a resting state. 92 and D1 (l60 to 100 %RIIR) , respectively, for the sedentary female subject category. The data for these patterns are shown in Appendix 3. Figure l4 is a plot of the high and low patterns. P can be derived directly from the hard data patterns R3 is calculated as follows: then, P = (i 60-140).3 + l40 = l46 P Q (152-138) . 1 + 138 = 142 ?2q - (140-133).3 + 133 = 135 P^Q = (132-127).3 + 127 = 128 P,^Q = (123-121). 3 + 121 = 122 Pgo'^ioo ^180 = (100-100).3 + 100 = loo. Since the series of tasks is ongoing, the predicted pattern must be placed in the appropriate time period. Therefore, P^ is at time 1 3 0 , P^^ at I6 0 , and so on, for total elapsed time of 240 seconds. A plot of H, L and P is shown in Figure l 4 . Table 7 presents the predicted cardiac response for the .subject emd the series of tasks of this example, as pro duced by the predictive model. The computer program and associated documentation for the predictive model are shown in Appendix 8 . TABLE 7 OUTPUT OF PREDICTIVE MODEL FOR THE SERIES OF FIXED INTENSITY TASKS OF THE NUMERIC EXAMPLE RESPONSE FOR************************* ______- FEMALE . -.. - - . ______SECENTARf RHR IS PC PCkER OUTPUT— -ELAPSED TIME...... MEAN HEAR I RATE PERCENT GF RESTING HEART RATE (kATTS) . .(SECONDS)...... (BEATS/MINUTE). 60_____ 0 - 80 100 60 10 91 114 60 20 96 121 60______30 ___ ICC 125 . 6 0 ______40... 102 12 7 ..50... 103 128 60 6 V _ 103 129 ICG 70 103 129 10 0 60 1 139 - 1 0 0 _____ 9 0 ___ 5 144 _\0 LO . 100 ...... 100... 7 146 110... 7 146 - 100 ______120 . 7 146 100 130 7 146 100 140 7 14 6 loO___ 7 146 160... 4 142 .0 170... ica 135 0 i « 0 __ 103 120 0 190 97 122 0 200 91 114 0. — ^ 1 0 ______07 1C9 0 2^0... 84 105 0 23 0... 82 103 0- 240___ 80 100 CHAPTER V ANALYSIS OF RESULTS This chapter, containing the analysis of the results, is divided into four discussion areas. First, the results and analysis of the work load to steady state %RHR relation ships are presented. Second, the hard data, collected for the purpose of supplying hard data patterns for the predic tive model, are interpreted and analyzed. Third, the pre dictive model is compared with previous models. Finally, the validity of the predictive model is investigated by com paring predicted results with observed results of the vali dation testing. Regression Analysis of Work Load to Steady State ^RHR In order to determine the level of %RHR at which an individual's heart rate could be expected to reach a steady state for a given work load, it was necessary to examine the relationship between work load and steady state %RHR. The independent variable was work load in watts and the depen dent variable was steady state %RHR. Simple linear regression was the technique used to examine the relationship, and a regression was run for each 94 95 subject category. The data points of Table 8 were plotted and the regression lines are shown in Figure 15. The regres sion equations are as follows: for MG: SS = .474w + 106.3 r = .95 r^ = .90 for MS: SS = .259W + 100.4 r = .99 r^ = .98 for FG: SS = .484w + 108.3 r = .97 r^ = .94 for FS; SS =: .431W + 103.0 r = .98 = .96 where : SS = steady state %RtIR W - work load (watts) r = correlation coefficient. The high correlation coefficients indicate that there is a strong linear relationship between work load and steady state /'oRHR for work loads requiring steady states of 100 to l60 %RHR. Although all correlations are relatively high, it can be observed that those of the sedentary subject categories are slightly greater than those of the subjects of good physi cal fitness. From the square of the correlation coefficient, the percent of the variance of steady state %RHR (SS) accounted for by the regression of SS on work load (W) can be determined. From 90 to 98% of the variance of SS is explained by the regression equations. The range of the regression coefficients, .225(.484-.2$9), is considerable. The slope of the FG equation is almost twice that of the MS equation. However, it can be observed from Figure 15 that the range of the regression coefficients. 160 FG 'Jig 150 - IS l40 0 0 vO 130 C 1/3 X «120 o w-p MS FG FS 110 - 100 È ' T— O 25 50 75 100 125 150 175 200 225 Work Load (watts) Figure 15 Steady state 5hRHR versus work load relationship for all subject categories. 95/0 confidence limits are shown for MS. TABLE 8 DATA FOR WORK LOAD TO STEADY STATE %RHR RELATIONSHIPS BY SUBJECT CATEGORY MG MS FG FS Wat t y SS %RHR Wat t s SS ?^RHR Watts SS 5oRHR Watts SS %RHR 0 100 0 100 0 100 0 100 0 100 0 100 0 100 0 100 30 120 50 114 20 120 30 120 30 120 50 118 25 125 37 115 50 133 60 120 37 132 40 120 50 138 100 120 37 132 75 l40 -v] 6o 140 150 133 60 l4o 75 l40 80 l48 150 137 65 l40 110 150 100 160 155 140 75 145 112 150 140 160 200 150 75 151 112 157 200 155 112 158 150 160 210 160 112 160 225 160 115 160 98 .053(.484-.43l), for MG, FG and FS is small. Because of the range of the coefficients and the cluster of the three high coefficients, each pair was examined to determine if signif icant difference exists. Only the confidence interval about the regression for MS was shown in Figure 15 in order to emphasize the difference between MS and the other three regressions. A "t" test (Crow, I9 6 1 , p. I6 1 ) was used to determine the significance of the regression coefficients of each pair (six in all) of equations. This procedure required the as sumption that the standard errors of the estimate for the two regressions be equal. An "F" test was used to show the equivalence of the standard errors. Table 9 shows the criti cal and computed values of F . As indicated in Table 9, the assumption that the standard errors are equal was shown to be true for all pairs. The programs written to calculate the necessary sums of squares for determining the "t" statistics are shown in Appendix 12. The hypothesis used for testing the regression coef ficient is the following: ” o- "1 = ” 2 where b^^ and b^ are pairs of regression coefficients. The results are shown in Table 10 and indicate that there is sig nificant evidence to reject the null hypothesis that the regression coefficient of the MG equation is the same as any one of the other three (MS, FG, FS), in favor of the alter native hypothesis, that they are not equal. The null 99 TABLE 9 CRITICAL AND COMPUTED VALUES OF "F" FOR TESTING THE NULL HYPOTHESIS THAT THE STANDARD ERRORS OF PAIRS ARE EQUAL .05 Level of Pairs F D.F. F .025 Significance MG-MS 3.44 3.28 Accent H 9,12 0 MG-F G 3.44 9,12 1.68 Accent H 0 MG-F S 3.78 9,10 2.34 Accent H 0 MS-F G 3.25 12,12 1.95 Accent H ^ 0 MS-F S 10, 12 1.42 Accent H 3.37 0 FG-FS 3.62 10,12 1.38 Accent H 0 TABLE 10 CRITICAL AND COMPUTED VALUES OF "t" FOR TESTING THE NULL HYPOTHESIS THAT THE REGRESSION COEFFICIENTS GF PAIRS ARE EQUAL VERSUS THEY ARE NOT Regression .05 Level of Pairs D.F. t Coefficients t .025 Significance MG-MS .474 2.09 4.76 Reject H .259 19 0 MG-FG .474 .484 -2.09 19 -. 16 Accept H ^ 0 MG-FS .474 .431 2.11 .12 Accept H 17 0 MS-FG .259 .484 - 2.07 22 - 5.99 Reject H^ MS-F S .259 .431 - 2.09 20 - 5.68 Reject H^ FG-FS .484 .431 2.09 20 1.10 Accept H 0 1 0 0 hypothesis was accepted for all pairs of regression coeffi cients not involving the MG coefficient. It can be concluded that the slope of the MS regres sion equation is one apart from the slope of the MG, FG and FS equations. This conclusion can best be explained by ref erence to the classical method of presenting cardiac responses to work load relationships. The classical method utilizes heart rate instead of %RHR. The regression lines for MG and MS for both the classical method and the method of this study are shown in Figure l6. The regression equa tions are as follows: for MG: SS = .^9W + 106.3 HR = .28W + 57.5 for MS: SS = .259W + 100.4 HR = .21W + 87.5 Wher e: SS = steady state %RHR HR = steady state heart rate. The MG regression coefficients are greater than the MS coefficients for both methods. It can be observed from Figure I6 that although sedentary males can maintain greater work loads for heart rates within the range of this study (230 watts at 160 %RHR for MS versus II5 watts for MG at 160 %RHR), the males of good physical fitness can be expected to maintain a greater work load at any given heart rate above the range of this study. The difference in the intercepts (87.5-57.5) is the reason that it appears the MS category is working more efficiently than the MG category. IVhen, in fact, those persons of good physical fitness have a l6o 120 MG 0) 150 MS 110 -HI \E n 4-» 0)d l40 100 S a 5 <0 « o +J 90 4-> d du 130 0) w MG as X -3 MS H d d a O -M 80 w-p H 120 •o d 110 60 100/ 50 25 50 75 100 125 150 175 Work Load (watts) F i g u r e l 6 . Work load to steady state %R1IR and heart rate for male of good physi cal fitness (MG) and sedentary male (MS). Note that MS regression lines are not extended to include the terminal points at 230 watts. 1 0 2 greater power output per beat increase (.28 vs. .21). The transformation from beats/minute to percent of resting heart rate (%RHR), although graphically confusing, does not alter this fact. Also, the power output per beat increase is greater for FG than FS (.30 versus .21). There is no statistical difference between regression coefficients for any pair of MG, FG, or FS. However, the cor relations for each of these regressions were very high, and it is expected that if it were in the scope of this study to examine enough subjects, a statistical difference would evolve. It is expected that by using a regression equation for each of the subject categories in the predictive model, a greater precision would result in determining the expected steady state %RHR. Analysis of Hard Data Patterns Introduction Analysis of variance was used to examine the transi ent responses of the twelve hard data patterns which were results of a step change in task intensity (four were steady state). The main effects and interactions are shown in the mathematical model of Chapter IV. The data for the twelve hard data patterns is pre sented in Appendix 3. Each data point in Appendix 3 (except for the steady state patterns A 1 , B2, C3 and D 4 ) is the cell mean for one subject category by time period. These patterns serve as the base patterns for the predictive model. All predicted heart rate patterns are extrapolated from these hard data patterns. The purpose for the analysis of variance 103 was to examine each pattern with respect to the two levels each of sex and physical fitness and the interactions of these factors. Since each pattern was a step change in heart rate over time, the time period factor was expected to be significant. The time period factor was included specifically for the purpose of obtaining a computerized output of cell means by time period; therefore, an analysis of the time period factor and interactions with the time period factor is not required. A complete summary of each of the twelve ANOVAs (ANOVA and EMS tables shown in Appendix 4) is presented in Table 11. It can be observed that the time period factor is significant for all tasks. The power of the F test in the ANOVAs was the same for both sex and physical fitness. In each ANOVA there were four subjects supplying two data points for each of nine time periods for a total of 72 data points for each treat ment level. Special charts (Pearson and Hartley, 1951» pp. 112-130) were used for calculating the power function for the analysis of variance test. The assumption was made that the experimenter was interested in detecting differ ences among means such that the largest difference is equal to one standard deviation of the error. It was determined that the power was .99 with a Type 1 error of .01. Analysis of ANOVA Results It is apparent from the ANOVA summary in Table 11 that, for the most part, the sex and physical fitness effect, and 104 TABLE 11 ANOVA SUMMARY (LEVEl, OF SIGNIFICANCE INDI CATE!1) Ma i n Effects and Intera étions Task SP T SP ST PT SPT A2 .01 A3 .05 . 05 .01 .05 . 01 A 4 . 01 . 01 .05 . 10 . 10 .01 B1 .01 B3 .01 B4 .01 .01 .01 Cl . 01 .01 .01 .05 C2 .01 C4 . 10 .01 D1 .01 D2 .01 .10 D3 .01 s = Sox p = Physical F itness T = Time Period 105 Lho .sex-physical fitness (SP) interactions were not signif icant. Most of the significant effects were for patterns which had initial values of 100 %RHR (A3 and A4). Only one SP inleraction was significant for patterns which had ini tial values of 1 2 0 / o R H R (B4). There were two significant main effects for patterns which had initial values of l40 %R1IR (Cl aii(i C4) and no significant effects for patterns which had initial values of l60 % R H R . There does not appear t;o be any special trend of significant effects or interactions. ]'igure 17 displays a plot of pattern A3 by sex. The significance is due mainly to the response of the male of good physical fitness (MG). Figure 25 (p. 115) shows the heart rate response by subject category. It can be observed that MG steady states at 2 0 seconds where MS and FG steady state at 5 0 seconds and FS at 7 0 seconds. It can also be observed that the MS and FG patterns are very similar. Figure 18 displays a plot of physical fitness patterns for task A3- Again, the significance can be attributed to the fast response to steady state of subject category MG. Figure 19 displays a plot of heart rate pattern A4 by physical fitness. Figure 26 (p.ll6) displays the heart rate response by subject category. It should be noted that, for both task A3 and A4, the responses to steady state are more rapid tor the subjects of good physical fitness than for the sedentary subjects. The MS response of task A4 was the cause of the significance of the physical fitness effect. There 160- 150 140 B a □ B □ = 130- o B Male 120- □ Female 8 110 100^ ■~T" " ' 1'" 1 - 10 20 30 4o 50 60 70 80 Time (seconds) 17. Plot of sex effect for task A 3 (/oUIll? t : Significance level is .0 5 . l6o 1 50 l40 O O e = 130 O 120 . ® Good 6 Sedentary 110 . 100 -è — r- > O 10 20 30 ko 50 * 60 70 80 Time (seconds) Figure I8. Plot of physical fitness effect for task A 3 (/oRIIR vs. time). Significance level is .05. A 160 - 1 no i4o - -130 O Good O Sedentary H O 0 3 120 110 - 100 10 20 30 40 30 60 70 80 Time (seconds) f 1gnre 19. Plot of physical fitness effect for iaslc A4 (5ofdlP vs. time). Significance level is .61. 109 Is a liiK'aj- trend for the MS response where the responses of the other three subject categories were very similar. Figure 20 displays a plot of the sex-physical fitness interaction for task A4. It can be observed that a definite interaction exists for each time period up to steady state. The degree of interaction is greatest at 40 and 50 seconds. At 50 seconds the FS response is at steady state and the FG response is still approaching a steady state. It is expected, and is true for most of the hard data patterns, that the MG and FG patterns accelerate to steady state more rapidly than the MS and FS patterns. The overlap in FG and FS patterns can also be observed in Figure 26 (p « U 6 ). The sex-physical fitness interactions are much more pronounced for task b4 than for A4. Figure 21 is a plot of the interactions by time period. Again, as in pattern A4, the FS response to steady state is more rapid than the FG response. There is no apparent explanation as to why the FG response accelerates to steady state more slowly than the P'S response for tasks A4 and B4, since in most step changes tlie opposi t e is 1.1'ue . Figure 22 displays a plot of patterns Cl by physical fitness. 1'^igure 30 (p. Il8) displays the heart rate responses by subject category. Again, the heart rates of the MG and FG subiect categories decelerate more rapidly to steady state than do the heart rates of the MS and FS categories. The plot tor sedentary subjects exhibits a strong linear trend. l6o 150 l4o 130. I-* □ o ■ MS O FG • FS 120 110 . 100 ~r~ T ^r— -r —r- T ”T“ M M M F M F M M M 10 20 30 >:0 50 60 70 Ti me ( s e coiid s ) Figure 20. Physical fitiie sex- ill t er-ac t i 0)1 for i'ark A4 (significance level is .05). Interaction is sliov/n for each t i me jrerioci. 1-ines connect subject categoric of similar physical fitness. 160- 130. □ MG ■ MS O FG H • FS 120 . 110 . 100 ■f — — 1 I II rnw n r ig W " ' —r —t— M M F M F M F M M M (sex) 10 20 30 40 50 60 70 Time (s ec ond s) Figure 21. Physical fitness--sex interaction for Task B4 (significance level is .01). Interaction is shown foi' each time period. Lines connect subject categories of similar physical fitness. lf-0 - ] "0 1 40 O Good O Sedentary O 130 M to 120 . 110 • e o o 100 o o 10 20 30 4o 50 6o 80 Ti in(! ( seconds ) 1 ; euro 22. Plot of physical fitness effect for Task Cl (%RHP vs. L i nie ) Si t ill f 1 canoe level is .10. 113 This trend is also apparent for MS and FS separately (see Figure 30)- The significance of physical fitness for task Cl can be attributed to the differences in cardiac responses for the female subjects since the responses of the male sub jects were very similar. Figure 23 displays a plot of heart rate pattern C-l by sox. Figure 32 displays the heart rate responses by sub ject category. The significance was only at the .10 level; however, the patterns for both FG and FS are numerically greater then those of both MG and MS for all data points from the initial value to steady state. The step changes in task intensity required a net change of either 20, 40, or 60 %RHR. It can be observed that those highly significant effects and interactions (.01 and .05 levels) are for tasks which have step changes of kO or 60 /oRHR. Certainly there is a greater potential for devia tion in responses for step changes of 40 and 60 %RHR than for step changes of 20 %RHR. All tasks which required step changes of kO or 60 ^RHR, except D1 and D2, resulted in at least one significant effect or interaction. Step Decreases in Task Intensity for Sedentary Subjects The predictive model does not include the prediction of cardiac responses to step decreases in task intensity for sedentary subjects when the initial value is greater than l^lO /oRllR and the expected steady state value is other than 1 □ 03 □ □ 1 5 0 o l4o 8 = 130: SB Male □ Female 120 110 ibO 115 □ M<'> P MS 150 O l'O • F S A A v e r a g e 1 4 0 130 120 A A à a A 110 lOO^L —I— 10 20 30 4 0 50 60 70 80 Time (seconda) Figure 24. Hard data pottern 3--Task A2. Subject category symbols not continued after steady state. 160 . 150 l4o □ A A ■ A 0 ▲ ,130 120. a o A □ M O ■ M S ? O KO 110 • FS A AvcM-nge 100 A —r— '■ I 10 20 30 4 0 50 f>0 70 80 T i m»' («ne nndm ) Kiguio 25, Ifrtid da in pn I loinh-.Tafik A 3, 116 I h O - D o o A 0 A □ A B o A î 40 D o S 1 JO □ N G Q M S O F G o FS A ''ver•nge 1 10 - 100A I— O 10 3 0 4 0 5 0 6o 70 HO Time (seconds) Fleure . Hard data pri 11 e rn s - - T a sk A 4 . ] Cy(4 150. 1 4 a □ M O B M S O FG e F S A Avcrn^e 1 3a 'A n I I r o 4 n o □ A □ B A A & A A lO 1!0 JO 4(1 70 no ,1.. I ■ l.ii'i «l.i I /I p/l I f c I r i - I lu. n.o . 117 1 so I'lO . o A A B = 130 . 120/1 □ M G a M S O F G • F S 110 /\ A v e r a g e 100 — I— 0 10 20 3 0 4 0 5 0 60 8o Time (seconds) Figure 28, Hard data patterns— Task B3. I tiO . D A A A B A B 1 5 0 . A D o a l40 A o B A o c l 3 0 5 120 G M G B M S O F G # F S ^ Avorogo 110. 1 f) V) /|() in no 80 I i me ( .s (u m I s ) i I 4.M t I i.'i I • I < 1.1 ( a ) j.i I I *' I n M _ - I /I s h 1 1 , iTiO 118 1 31) . a Mr, B O FC. • FS A A v e r a g e I '10 A 130 B 120 ë ■ o A a 110 ■ « B è m 100 è 10 20 30 4o 50 60 7 0 80 Time (seconds) Figure 30. Hard data pat torns-.Task Cl. 160 • D M G B M S 1 5 0 1 O F G • F S A A v e r a g e I'lO A o A 130 . 0 m A B ❖ B 0 & I A I 0 If) flf) 70 80 I t Ml* • ( M #M M t |t I M ) I j j 111 * ' ^ ^ • 11 /1 I 11 i l l I n 11. j I I » ' I n •< — — I M K ( «2 « 119. 11.0 a A o A l'iü A i l'io £ 130 § □ MG 120 B NS O F G . F S A A v e r a g e 1 10 100 10 20 30 4 0 50 60 7 0 80 Time (seconds ) F i g u r e 32. H a r d d a t e p n 11 ern.s--Task C4. l6o o M G 150 . B M S O F G • F S A A v e r a g e 1 4o g ç ] 30 2 ▲ g 1 20 n A a ■ 110 . A • ■ • n o è A 10(1 0 □ 0 1 o LiO 30 ^0 10 f,o 70 80 r i lin* ( s ( o *4 ) j !. I I.u 'I I la t /» I i.H I •• I n - I a M k l'I ; 120 Ificv □ MO H M S O I'O AO ® F S 110 □ A A v e r a g e 4 □ A I 'iO - □ o A □ B o q: 130 2 a A o A A □ 9 9 120 ' 110 l o o j I------1------1------r------'— — r— 0 10 20 30 4 0 50 60 7 0 80 Time (seconds) Figure 34. Hard data patterns--Task D2. ' Ibol 130 A A 8 A A l4o a a o A 130 □ M G 120 g MS O FG • F S A Average 110 100 / ' I 10 20 30 4 0 10 Go 70 80 I i me ( *4e« (iiifl M ) I » J ' M m I IJ 11M 1 /> p n f I p r'li M - - I M M k M J. 121 100 %RHR. Although the predictive model includes the mecha nism for handling this circumstance, the necessary hard data patterns could not be obtained through experimentation with consistency for sedentary subjects. Only one subject in each of the sedentary categories produced patterns D2 (l60 to 120 %RHR) and D3 (l60 to l40 %RHR). The cardiac response of the other subject in each category was such that steady state values of 120 and l40 %RHR were not realized within the time limit for each task (l80 seconds). Since only one of the two subjects in each of the sedentary categories reached a steady state within the time limit, step changes for sedentary subjects which required hard data patterns for tasks 02 and D3 cannot be accommodated by the predictive model. The hard data patterns D2 and D3 for MS and FS of Appendix 3 represent only those responses of the subjects who did realize respective steady states of 120 and l40 %RHR. How ever, those patterns were not included in the predictive model. The most probable cause of the lag in decrease to steady state for the two subjects was that they were exer cising above their respective aerobic capabilities. The tasks were designed such that, according to the literature, no task required an anaerobic contribution at steady state. However, although the heart rates for these subjects were below the maximum aerobic heart rate (Sstrand, 1971, p. 132) of 134 beats/minute for males and I38 beats/minute for females, their heart rates at 16O %RHR were within five beats/minute of these heart rates. The maximum heart rates presented by Rstrand are averaged figures and intended to represent the 122 ■whole population for the age group of this study. These two subjects were probably exceptions and were exercising at the limits of or above their aerobic capacities. In order to investigate this possibility, two sedentary male subjects were tested to determine if they were exercising above aerobic capacity at l60 %RHR. The necessary work load of 230 watts was derived from the steady state %RHR to work load relationship for sedentary males. Each subject performed the task and the oxygen uptake was measured for both exercise and recovery to a resting state. By making the ordinate oxygen consumption instead of %RHR in Figure 7 (p. 27), the reader can more easily understand the compari son. The ratio of oxygen debt (Area A) to oxygen payback (Area B ) for one subject was approximately 1.0 and approx imately 2.1 for the other. This observation indicates that one MS subject required an anaerobic contribution where another did not. Both the hard data patterns and the oxy gen consumption test indicate that sedentary subjects are on the border line of aerobic capacity at 16O %RHR. Since the cardiac responses to tasks D2 and D3 are not produceable by all sedentary subjects within the time span of this study, the hard data patterns were not included in the predictive model. Comparative Analysis of Hard Data Patterns The statistical analysis of the hard data patterns indicated that the proper use of the hard data patterns would be to use only the averaged patterns for the predictive model, thereby eliminating the need for hard data patterns 123 by sex and physical fitness. However, a statistical anal ysis in itself is not sufficient to describe the hard data patterns. Certain observations led this writer to believe that further testing and larger sample sizes would result in hard data patterns by subject category which are signif icantly different. These observations are presented in the following discussion. Subject Category versus Averaged Hard Data Patterns Table 12 shows a '■«-’.iparison of predicted results by averaged hard data patterns and by hard data patterns for subject categories. The observed and predicted results are shown for the first step change of series four. This par ticular step change was selected for comparison since only a portion of the transient response was predicted for all subject categories, and the work load was great enough to effect a considerable cardiac response (100 to l46 %RHR). It can be observed by examining the errors (eg and e ^ ) of Table 12 that the predictions using hard data patterns by subject category (Pg) were more accurate than the prediction; using averaged hard data patterns. In only two of the twelve time periods presented (MS-20, FG-20) was more accurate than Pg when compared to the observed heart rate value. These results indicate that the exclusive use of averaged hard data patterns for the predictive model would reduce the accuracy potential of the predictive model. 124 TABLE 12 COMPARISON OF PREDICTED HEART RATES USING HARD DATA PATTERNS BY SUBJECT CATEGORY ( P g ) AND BY USING AVERAGED HARD DATA PATTERNS ( P ^ ) . THE OBSERVED (0) AND PREDICTED HEART RATES ARE FOR THE FIRST STEP CHANGE OF SERIES FOUR. Subject Time 0 Cat egory (sec) (beats/min) ^S ( P g - O ) ^A ( p ° - 0 ) MG 0 58 58 0 58 0 10 69 69 0 67 -2 20 8o 79 -1 74 -6 MS 0 76 76 0 76 0 10 88 86 -2 88 0 20 95 94 -1 98 3 FG 0 72 72 0 72 0 10 85 85 0 83 -2 20 93 92 -1 92 0 FS 0 80 80 0 80 0 10 90 92 2 94 4 20 95 99 4 103 8 125 Analysis by Inspection of Plotted Hard Data Patterns An analysis by inspection of the plotted hard data patterns of Figures 2k through 35 on pages 115 through 120 is required to fully develop an argument for using hard data patterns by subject category. The following discussion addresses trends within and between hard data patterns by subject category. It is interesting to note that for step changes of 20 %HHR in hard data patterns A2, B1, and B3, those of MS accelerate or decelerate ro steady state more rapidly than those of MG. This is graphically displayed in Figures 24, 271 and 28. However, for step changes of 20 %RHR with greater initial values (l40 %RHR), the acceleration to steady state is more rapid for the MG category (see Figures 31 and 32). This leads to the conclusion that for ongoing exercises of light (approximately 120 %RHR) work loads, the heart rate patterns, realized for a small step change of approximately 20 %RHR, accelerate to steady state more rapidly for seden tary males. For ongoing exercises of moderate (approximately l40 %RHR) work loads, the opposite is true. For all step changes of 40 to 60 %RHR, the response to steady state is more rapid for males of good physical fitness than for seden tary males. In comparing responses for FG and FS categories, there appears to be only one consistent trend. For all hard data patterns for recovery to a resting state (Bl, Cl and Dl), the elapsed time to steady state is at least 20 seconds less for FG than for FS. These responses are displayed in Figure 126 27, 30, and 33- Tliis is not true for the male subject cate gories. In this case, the elapsed time to steady state is 30 seconds less for MS than MG for recovery from light exer cise (see Figure 27) and 30 seconds more for MS than MG for recovery from moderate exercise (Figure 33)» The responses are similar for light to moderate exercise (Figure 30). Most of the heart rate patterns for step changes in work load were nonlinear. However, the heart rate response for the sedentary males exhibited definite linear trends for almost all of the step changes. These trends are visually apparent in Figures 25, 26, 27, 29, 30, 31, and 32 of pat terns A3, A4, Bl , B 4 , Cl, 02, and C4. It is apparent from these observations that there exist certain consistent trends within and between the hard data patterns which are not portrayed in a statistical anal ysis. Since these trends do exist, and since the predictive model has a greater accuracy potential (see preceding sec tion) by using hard data patterns by subject category, the hard data patterns utilized in the predictive model are by subject category. Comparison of the Accuracy of Various Predictive Models Differences between Previous Models and the Predictive Model There were three predictive models presented in detail in Chapter II which were developed by Schilpp, Suggs and Vogt. There are several apparent differences between 127 these previous models and the model of this study which need to be addressed before comparing the predicted heart rate patterns of each. The first, and perhaps most significant difference, is that for any given work load and resting heart rate, the predicted heart rate pattern will be the same for all persons, regardless of sex or physical fitness. It becomes readily apparent that this approach is questionable when it is consid ered that many sedentary females or females of good physical fitness are incapable of steady state heart rates at a work load of 200 watts. Whereas, even sedentary males are capa ble of maintaining steady state heart rates at a work load of 200 watts. None of these models has the capability of linking heart rate patterns for an exercise with a series of step changes in task intensity. Each model can predict only one step change at a time. The results in Table 13 were compiled by predicting the increasing step change, and then predict ing the recovery to a resting state. The two patterns were then linked together manually. Another difference is that only Vogt described a definitive mechanism for determining the expected steady state heart rate for a given task. Neither Suggs' nor Schilpp's model can make a priori prediction of heart rate patterns since the exercise must be completed and the steady state heart rate recorded before a "prediction" caxi be accomplished. 128 However, the author of this paper augmented and refined each of these studies such that a priori prediction would be possible. Since each of these models is mathematical in form, each is dependent on time constants. The time constants depict the elapsed time for heart rate to reach a steady state. There is only one time constant for Schilpp's model; therefore, the time to steady state is the same for all work loads. There are onlv three levels of time constants for Suggs' model; therefore, only three times to steady state. Vogt's model is the only model where the time con stant is dependent on the task intensity and resting heart rate, and therefore, varies accordingly. It might also be noted that none of the authors submitted a formal definition of resting heart rate. Yet, each model required resting heart rate as an input variable. The computational aspects of the predictive model of this study are more complex than those of the previous models and require the use of a computer to store and select the appropriate hard data patterns and to compute a predicted cfirdiac response to exercise. It is possible to compute a predicted cardiac response by hand (see Chapter IV), but I fie procedure is l ong and tedious and requires a computer for all practical purposes. Tirere is a detailed comparison of the approach and methodology of the previous models presented in Chapter III. 129 Comparison of Predicted Cardiac Response 1 n t.roduc t ion 'Phe predictive models of Schilpp, Suggs , and Vogt were incomplete as presented in their respective papers. In order to obtain actual predicted results, it was necessary for the author of this study to augment and, in some cases, make corrections to these previous predictive models. This was done so that a comparison could be made between the out puts of the previous mode“.'_ and the output of the predictive model of this study, referred to as the predictive model. Interactive computer programs were written to accom modate each of the models such that the input variables for all models would be comparable. Since the cardiac response to only one step change in task intensity can be predicted for each of the previous models, the input variables are resting heart rate, duration of the task and work load, ihe interactive computer programs, output of predicted pat terns, and associated documentation are presented in Appen dices 9, 10 and 11 for models of Schilpp, Suggs and Vogt, respecti vely. The observed results of series three of the valida te on testing were compared to the predicted results of all piedictive models. Series three was selected for several reasons. First, series three consists of only two tasks, the second of which is recovery to a resting state. It is required that the second task be to resting since Schilpp's 130 model does not acceiJt decreasing step changes to other than a zero work load. Also, the three previous predictive models are very limited in their respective capabilities to predict cardiac response at low work loads because of the limitations o t the time constants, therefore, series three was selected because of the relatively high work load. When the observed results of all series of validation testing were compared to the results of the predictive model of this study (detailed analysis in following section) it was determined that for every subject category the predicted results of series three compared less favorably to the observed results than any of the other five sei'ies (based on mean error and standard deviation of the error). Therefore, so as not to bias the comparison of the predictive models, the least favorable results of the predictive model of this study were used. The predicted results and the observed results are presented by subject category in Tables 13, , 15, and l6. The error (predicted minus observed) is shown for the previ ous model which exhibited the best estimates of the observed heart rate values. Also, the error is shown for the predictive model of this study. Mean, standard deviation, and range are presented for each column of errors. Analysis The following discussion is an analysis of the results of the various predictive models. The results are discussed by subject category. TABLE 13 PREDICTED AND OBSERVED CARDIAC RESPONSES FOR SERIES 3-MG. THE ERROR (PREDICTED MINUS OBSERVED) IS SHOWN FOR THE BEST PREDICTION (SCHILPP, SUGGS, VOGT) AND FOR THE PREDICTIVE MODEL. Work Schilpp's error Suggs' V o g t 's Predictive error Time Observed Load Mode I ( P-0) Model Model Model ( P-0) 0 105 58 0 58 60 58 0 58 10 105 74 -2 64 66 69 -7 76 20 105 80 -7 80 70 78 -9 87 30 105 84 -3 89 74 85 -2 87 4o 105 87 0 98 78 90 3 87 50 105 90 3 105 81 91 4 87 60 105 92 5 112 83 91 4 87 6 84 4 70 105 93 117 91 87 H 8o 105 95 8 123 86 91 4 87 90 105 96 9 128 89 91 4 87 100 105 97 10 132 91 91 4 87 110 0 97 21 132 92 78 8 76 120 0 88 23 128 91 77 12 65 130 0 81 21 123 85 71 II 60 l4o 0 76 18 118 80 66 8 58 150 0 72 I4 113 76 64 6 58 i6o 0 69 II 108 72 61 3 58 170 0 66 8 I04 69 59 I 58 180 0 64 6 lOI 66 58 0 58 190 0 63 5 97 64 58 0 58 200 0 62 4 94 62 58 0 58 210 0 61 3 91 60 58 0 58 220 0 60 2 88 59 58 0 58 230 0 60 2 86 58 58 0 58 240 0 59 I 84 57 58 0 58 Mean 7.0 2.3 S.D. 7.9 4.8 Range 30.0 21.0 TABLE Ik PREDICTED AND OBSERVED CARDIAC RESPONSES FOR SERIES 3-MS. THE ERROR (PREDICTED MINUS OBSERVED) IS SHOWN FOR THE BEST PREDICTION (SCHILPP, SUGGS, VOGT) AND FOR THE PREDICTIVE MODEL. Work Schilpp's error S uggs' V og t 's Predictive error Time Observed Load Model ( P-0) Mode 1 Model Model (P-0) 0 220 76 0 76 80 76 0 76 10 220 111 23 96 110 90 2 88 20 220 123 28 114 129 95 0 95 30 220 131 28 131 142 102 -1 103 4o 220 138 27 145 150 106 -5 111 50 220 143 25 158 155 111 -7 118 60 220 147 158 120 27 169 115 -5 H 70 220 151 29 180 160 119 -3 122 VjO 80 220 153 31 188 161 120 -2 122 K) 90 220 155 33 197 162 120 -2 122 100 220 157 35 203 163 120 -2 122 110 0 154 37 210 163 120 -2 122 120 0 148 37 190 143 111 0 111 130 0 l4 o 29 181 130 104 -5 109 l40 0 125 17 172 120 96 -12 108 150 0 ll4 9 165 110 90 -15 105 i6 o 0 106 4 158 104 87 -15 102 170 0 99 0 151 98 84 -15 99 IBO 0 94 -1 145 94 82 -13 95 190 0 90 0 l4o 90 81 -9 90 200 0 86 -2 135 88 79 -9 88 210 0 84 -1 130 85 78 -7 85 220 0 82 2 126 83 76 -4 80 230 0 80 1 122 81 76 -3 79 240 0 79 1 118 80 76 -2 78 Mean S.D. Ik,7 5.2 Range 39.0 17.0 TA LU E 15 PREDICTED AND OBSERVED CARDIAC RESPONSES FOR SERIES 3-ES. THE ERROR (PREDICTED MINUS OBSERVED) TS SHOWN FOR THE BEST PREDICTION (SCHILPP, S 1,0 OS , VOGT) AND FOR THE PREDICTIVE MODEL. Work 5chiIpp's error Snggs' V o g t 's Pr ed i c 11 ve error Time Observed Load Mode 1 ( p-0) Model Model Mo del ( P-0) 0 125 8o 0 80 82 80 0 80 10 125 100 12 91 98 95 7 88 20 125 106 12 101 108 106 12 94 30 125 111 11 110 115 113 13 100 4o 125 115 10 118 120 118 13 105 50 125 118 7 125 123 123 12 111 6o 125 120 0 131 125 125 5 120 70 125 122 -3 137 126 125 0 125 8o 125 124 -1 142 128 125 0 125 90 125 125 0 l46 129 125 0 125 100 125 126 1 150 129 125 0 125 110 0 127 2 154 129 125 0 125 120 0 127 2 152 119 120 0 120 130 0 ll6 2 147 113 111 -3 114 l40 0 108 0 l4o 108 105 -3 108 150 0 101 9 135 103 98 6 92 160 0 97 12 130 99 91 -6 85 170 0 93 13 125 97 87 -9 80 l80 0 90 10 121 94 84 -4 80 190 0 88 8 117 92 82 2 80 200 0 86 6 113 90 80 0 80 210 0 85 5 110 88 80 0 80 220 0 84 4 107 87 80 0 80 230 0 83 3 104 86 80 0 80 240 0 82 2 103 84 80 0 80 5.1 2.9 S.D. 4.9 5.1 Range 16.0 17.0 TABLE 16 PREDICTED AND OBSERVED CARDIAC RESPONSES FOR SERIES 3-FG. THE ERROR (PREDICTED MINDS OBSERVED) IS SHOWN FOR THE BEST PREDICTION (SCHILPP, SLOGS, VOGT) AND FOR THE PREDICTIVE MODEL. Work Schilpp's Suggs' V o g t 's error Predlet ive e rror Time Ob s er \' e d Load Model Model Mode 1 ( P-0 ) Model ( p-0 ) 0 100 72 72 73 1 72 0 72 10 100 88 81 86 -2 85 -3 88 20 100 93 96 94 -4 93 -5 98 30 100 97 98 99 -8 99 -8 107 4o 100 100 105 103 -1 104 -6 110 50 100 103 111 106 -4 108 -2 110 60 100 105 117 107 -3 110 0 110 70 100 106 122 109 -1 110 0 110 80 100 107 126 110 -1 110 -1 111 90 100 108 130 111 0 110 -1 111 100 100 109 133 111 0 110 -1 111 110 0 110 137 111 0 110 -1 111 120 0 101 132 104 -2 io4 -2 106 130 0 95 128 99 0 91 -8 99 l40 0 89 123 95 7 88 0 88 150 0 85 119 88 9 83 4 79 160 0 82 116 86 13 78 5 73 170 0 79 112 84 12 73 1 72 180 0 78 109 82 10 72 0 72 190 0 77 106 80 8 72 0 72 200 0 75 103 79 7 72 0 72 210 0 74 100 78 6 72 0 72 220 0 73 97 77 5 72 0 72 230 0 72 94 76 4 72 0 72 240 0 72 91 75 3 72 0 72 M e a n 2.3 -1 . 1 S.D. 5.5 3.0 R a n g e 21.0 13.0 135 The predicted and observed results for series three, male of good physical fitness, are presented in Table 13- Jt can be observed that of all the previous predictive models, none exhibited a steady state for either exercise or recovery ■within the time span of each task. ^Vhereas , the observed elapsed times to steady state for exercise and recovery are 20 seconds and 40 seconds, respectively. Since there ■were no steady state values exhibited for any of the previous pre dictive models, the inaccuracies would be greater if the dur ation of the exercise task was longer. Both Schilpp's and Vogt's output appeared to be leveling at about 100 seconds. Tlie accuracies of Schilpp's and Vogt's models were approximately equivalent. However, the standard deviation of Schilpp's output, 11.1 (not shown in Table 13), was suf ficiently greater than that of Vogt's, 7.9, to conclude that Schilpp's output is the best of the three previous models. The output of Suggs' model exhibited as much as 63 beats/ minute error. The overprediction of Schilpp's model is sub stantially greater than that of the predictive model (7«0 versus 2.3 beats/minute). There is also a broader dispersion of error for Schilpp's model than for the predictive model (standard deviations of 7»9 versus 4.8). Based on the preced ing comparisons, the predictive model was more accurate than the three previous models. The predicted results of the previous models for series three, sedentary male, are the most inaccurate of the 136 results of the four subject categories (see Table l4). It can be observed by inspection that none of the three were even close, as all were overpredictions. Schilpp's model was slightly more effective than Vogt's but still exhibited a mean error of 16.6 beats/minute and a standard deviation of 14.7 beats/minute. At one standard deviation the error could be from 20 to 50 percent of the observed value. For the predictive model, the error at one standard deviation could be from 7 to 12 percenr of the observed value. It should be noted that the mean error and standard deviation of the error of the predictive model results for Series 3-MS were greater than all other series investigated (24 in all). The most accurate predictions of the previous mod els were made for series three, female of good physical fitness. These results are shown in Table 15 « Again, however, the output of Suggs' model was not comparable to that of Schilpp's and Vogt's in terms of accuracy. Vogt's model exhibited a steady state heart rate for exer cise equal to that of the observed, and was therefore con sidered more accurate than Schilpp's output. Again, the error means indicate a slight overprediction for Vogt's model (2.3 beats/minute) and a slight underprediction for the predictive model (-1.1 beats/minute); therefore, the mean error does not provide the necessary information for a conclusion as to which is the best prediction. However, the standard deviation of the error (5 « 5 v s . 3 « 0), indicates 137 that there is a greater dispersion of error for Vogt's model. At one standard deviation, the error for Vogt's prediction could 1)0 from 7 to 13 percent of the observed; whereas, the error for the predictive model would be only 3 to 7 percent. Also the range of errors is considerably greater for Vogt's model (21 vs. 13 beats/minute). Table l6 presents the predictions for series three, sedentary female. Schilpp's and Vogt's model again prove to be t he best of the three previous models. Both are over predictions, with mean errors of 5*1 for Schilpp's model and 7.6 (not shown in table) for Vogt's model. Schilpp's model was used for comparison to the predictive model since the moan error was less than that of Vogt's model. The observed results indicate a steady state heart rate of 125 beats/minute at 70 seconds, and the predictive model results indicate a steady state heart rate of 125 beats/minute at 60 seconds. The results of Schilpp's model do not indicate a steady slate heart rate. This would imply that the error would increase with an increased duration for the exercise. Since the standard deviations (4.9 vs. 5.1) and ranges (l6.0 vs. 17.0) are approximately the same, the error means can be com pared directly. The overprediction for the predictive model (2.9) is less than that of Schilpp's model (5.I). This fact, coupled with the fact that Schilpp's results do not reach a steady state value, indicates that the predictive model presents a more accurate prediction. 138 Conclu s ion .s Certain conclusions can be drawn from the predicted results of the three previous models. It was apparent for all subject categories that the predicted results of Suggs' model were far less accurate than those of Schilpp's and Vogt's model. It can also be noted that of the three, Schilpp's model was most appropriate for predicting cardiac responses, since Schilpp's model was shown to be more accurate for three of the four subject categories. The results of the predictive model were shown to be more accurate than the best effort of the three previous models for each subject category when compared to observed heart rate responses. Again, it should be noted that the predicted results of the previous models, shown in Tables 13, 14 ,1 5 , and l6 apply to any individual regardless of physi cal fitness or sex. For example, in an actual test a seden tary male performed the exercise of Table 15 for a work load of 125 watts and realized a steady state of lOB beats/minute. It is apparent that the results of the previous models (126, 154 and 124 beats/minute) are erroneous for a sedentary male. The results of this comparison render sufficient evi dence to conclude that the predictive model can more accur ately predict cardiac response to exercise than can previous models. The predictive model also exhibits a greater flexibility in that there are allowances made for sex and physical fitness and it can predict the cardiac response to a series of step changes in task intensity. 139 Evaluation of Predictive Model Introduction This section is a discussion of the validity of the predictive model. The observed data of validation testing are compared with the predicted values from the model. The results are discussed by time periods, by subject category and series. The results of the predictive model were com pared to the observed data by examining the error (predicted value minus observed valu^V. Exercise Series of Validation Testing A subject from each of the four subject categories performed six exercise series. Each series consisted of two or tliree tasks. The tasks and their respective durations are shoim in Table 17» It can be observed that although the durations are the same, the work loads vary between subjects for each series. The series were selected such that the expected cardiac responses would be similar in terms of %RHR. The steady state %RHR to work load relationship varies between subject category, consequently, the work loads vary within a series. The predicted and observed values by subject category and series are presented in Appendix 7. Figures 37 tlurough 60 show plots of the predicted and observed val ues . 140 TABLE 17 EXERCISE SERIES FOR VALIDATION TESTING WITH DURATION AND INTENSITY OF RESPECTIVE TASKS Subject Categories Series Seconds MG MS FG FS Watt s Watt s Watt s Watts 1 70 50 110 45 60 70 85 175 Bo 100 100 0 0 0 0 O 30 30 75 25 40 100 60 135 55 75 110 40 90 35 50 3 110 105 220 100 125 130 0 0 0 0 h 30 85 175 Bo 100 110 0 0 0 0 100 20 60 15 30 5 100 0 0 0 0 130 40 90 35 50 10 60 135 55 75 6 20 65 145 6o Bo 140 40 90 35 50 80 0 0 0 0 l4i Distribution of the Error The two sample problem of evaluating the predicted values against the observed values was condensed to a one sample problem by considering the error (predicted minus observed). The sign of the error relates whether the model is overpredicting (positive error) or underpredicting (negative error). The standard deviation and range of the error were used in conjunction with the mean error in order to determine accuracy in predicting and to estimate the maximum error. The distribution of the error data for all vali dation testing is displayed graphically in the histogram in Figure 36. The error data is presented in Appendix 3 by series for each subject category. A Chi-square goodness-of-fit test was used to determine if the error distribution was distributed normally with mean equal zero. The calculated Chi-square value with 27 degrees of freedom was equal to 1?0. This value was much greater than the critical value of 44 at the .05 level. Conse quently, it was concluded that the error distribution was not normal. However, there is a definite central tendency to zero, and there are certain characteristics exhibited which are associated with a standard normal distribution. rIN = -li.OOCiCOC HiX = 15.000000 -13.C -Ij.u -11.0 -9.0 -I.') -1.0 -J.O -l.O 1.0 J.O 5.0 7.0 9.0 11.0 13.0 15.3 17.0 19 .0 -14.0 -12.0 -lo.O -o.O -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 B .0 10.0 12.0 14.0 16.0 18.0 ..*66...+++...66*...66*. 20.. 0 200 .0 14 6,0 196..0 192.0 192.. 0 1 c £ .0 186., 0 164.0 184.,0 1 e .. 0 180..0 176 .0 1 76..0 1 7 2 . 6 172..0 I 6 P . 0 168..0 1 6 4 . 0 164.,0 16C.C 160..0 156.6 156..0 152.0 152.,0 I 4P.I 1 4 3 .,0 144.0 144., 0 tfi 14C .0 143.,0 136.0 136. 0 o 132.0 1 32.,0 •H 1 2 c . 0 123.,0 •P 124.0 124. 0 (S 1 2 6 .0 120. 0 > 116.0 u 116. 0 o I 12.0 112. 0 (0 loe. j 108. 0 1.4.0 104. 0 o IOC .0 103. 0 9 6. C 96. 0 tH H 92.0 92. 0 o f 88.Û 88. 0 03 84.0 84. 0 u fcC .0 80. 0 0 76.0 76. 0 72.0 72. 0 f e . j 1 68 . 0 % 6 4 . 0 64. 0 6C.C 60. 0 56.0 56. 0 52.0 52. 0 46.0 48. 0 44.0 44. 0 40.0 40. 0 36.0 36. 0 32.0 32. 0 26.0 28. 0 24.0 1 24. 0 20.0 1------2 0 . 0 16.0 1111111- 16. 0 12.0 llllllllll-- 12. 0 0.0 ------Ill 1111111111111 -- 8. 0 4.0 — II1111111111 1111,11111111 11 1- 4. 0 6 6 *...*♦ 6 ,..6 6 *. ..66 6 ...***...6 *6...** 6... 66...66*...***. -15.0 -13.6 - 11 .0 -9.0 -7.3 -5.0 -3.0 - 1.0 1.0 3.0 5.0 7.0 9,0 11.0 13.0 15.0 17.0 19 .0 -14.0 -12, 0 - 1 0 . — 8.0 -6.0 —4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 Error (predicted- observed) Figure 36. Histogram showing distribution of error (predicted minus observed) over all time periods and all series. 143 Although the mean is -.7795, the mode is zero (l60 of 576 observations). The standard deviation of the error is 3.6681. Using a mean of zero, the error distribution compares favorably the normal distribution with 79%, 97%, and 99% of the observations within one, two and three standard deviations, respectively. This compares to 68%, 98% and 99.8% for the normal distribution. The "t" sta tistic used in the following analysis is appropriate if the sample comes from a rurmal population which is "within a reasonable degree of approximation" (Miller, Freund, I96 5, p. 164). Since the error distribution exhibits certain properties of normally distributed data, the error distri- buti on can be considered a "reasonable approximation" to the normal distribution. It can be observed from Figure 36 that there were 28 underpredictions of more than 6 beats/minute and 28 over predictions of more than 6 beats/minute. These 56 observa tions comprise approximately 10% of the total. Based on the total error data, it can then be surmised that the error at any point in time will be 6 beats/minute or less, 90% of the time. The heart rate responses investigated in this study ranged from approximately 60 to I30 beats/minute. Therefore, the error as a percentage of heart rate could be as much as 10% for 60 beats/minute to less than 5% for I30 beats/minute. 144 Conséquently, ^0% of the time a user of the predictive model could expect errors in predicted output to be no more than l/u to 10% of the observed heart rate value. Time Period Analysis The predictive model produces estimates of expected heart, rate responses over time using only resting heart rate as a point of reference. This section discusses the possi bility of increasing error over time. The approach selected for this analysis was to i_.ivide the series into four one minute time periods. By this approach, the relative accuracy for predictions in each time period can be determined. All validation data was included in the analysis of time periods. The error data is presented in Appendix 5 and analyzed by time period in Table l8. Time period one is the first minute, time period two, the second minute, etc. It can be observed from Table l8 that the mean error for each time period is negative indicating an underprediction. Upon testing the hypothesis that the mean error is equal to zero, it was determined that only the mean error of time period one could be considered equal to zero. The null hypothesis was rejected in favor of the hypothesis that the mean was not equal to zero for all other time periods. It can be noted that the standard deviations of both time periods two and four were less than the standard deviation of time period one. This would indicate that the potential error at one standard deviation would be greater in time period one Ut A Time Periods o INTERVAL •ri ■P flS Ib.OOO ) 4 > * * k 12,000 0) 9.0 00 - ' ■ " OJ ü . 0 0 0 ***#-* 0.0 o “ ü , 0 0 0 (H -e, 000 « é * * * * * 1 • * «r * * * * * ********** ***** O - 12.000 * * * * * * -16.000 ) *** * . O ME. AN -0.29g - 1.201 -1 .niü - 0 , 6 0 a underlined means significantly s DEV Ü.05Ü 2.Mis ü.idO 3.062 different than 0 at .05 level N laa. l«ü. lüu. ALL GOü'jPS CQMei^tO SUM Cicr SOUACtS DF MEAN .6: u A 3 E F RATIO ME ?-:t.nEEN 70." A22 3 23.6607 1.7596 S DEV 3.6681 WITHIN 76 65.66M1 572 13.U015 H MAXIMUM 16.0000 TOTAL 7736,a063 575 f - ^ ' MINIMUM ■15,0000 vn TABLE 18. HISTOGRAMS AND DESCRIPTIVE STATISTICS FOR TIME PERIODS 1 (0 to 60 SECONDS), 2 (60 to 120 SECONDS), 3 (120 to l80 SECONDS), AND 4 (l80 to 240 SECONDS), F RATIO'TESTS HYPOTHESIS THAT THE MEANS ARE EQUAL. NOTE: HISTOGRAMS ARE PRESENTED HORIZONTALLY. l46 than in two and four (-4.34 compared to -3 « 94 and -3 » 66 beats/rninute ) . It would appear that the greatest poten tial error would occur in time period three, since the differences from zero, as well as the standard deviations, are the greatest. The F ratio of Table l8 tests the hypothesis that the time period means are equal. Since the value of the F ratio is less than F (.05, 3,592) (1.759 <2.60), there is no statistical evidence to indicate that the means are different. There is very little difference in the stan dard deviations of the four time periods (2.94 to 4.38 for a range of error of -15 to +15)- Considering only the means and standard deviations of the time periods, cer tainly there is no evidence to indicate that there is a significant difference in the error produced for each of the time periods. It might also be noted from the histo grams of Table l8 that for every time period, the distri bution of the error is such that 84 to 91 percent of the errors are within the interval of -6 to 2 beats/minute. This observation also indicates a uniformity in the dis tributions . It can be concluded that there is no reason to sus pect that the predictive model will compound in error over the four minute time period of this study, nor is there reason to suspect that the distribution of the error for any time period is different than that of another. 147 Statistical Analysis by Subject Category A subject in each subject category performed six series of exercises consisting of step changes in -work loads- Tables 19 and 20 present a histogram showing the distribu tion of the error for each series, and the mean and standard deviation for each series. Descriptive statistics for the combined series for each subject category are also presented. For analysis of data of this kind, straight forward ap proaches do not exist which result in statistically conclusive evidence that the predicted output for one series or subject category was superior to that of another series or subject category. However, certain conclusions become apparent by inspection of the means and standard deviations, and by inspection of the plots of observed and predicted heart rate responses of Figures 37 through 60 (pages 153-166). Observe from the F ratios displayed in Tables 19 and 20 that for each subject category the hypo thesis that the means are equal is rejected in favor of the hypothesis that they are not (F(.05,5 ? 138) = 2.21). This finding was expected because of the diversity in configura tions (task intensities and durations) of the six series. The magnitude of the F ratio renders insight as to the range of mean errors. The range of series means is greatest for the sedentary subject categories. The ranges are 3*7 and 1.8 for NG and FG, and, 5.1 and 4.4 for MS and FS, respectively. The range of means is a direct indication of the stability ISTÇRVAL Series J - f J cl.C^CO ) 1 IF .COO ) n l ' . - O O 1* CO 12.030 I* ** ■H- 9-O00 ) +J 6,003 ï* $ ' 3,uOO ï* * $$ > :.0 «#6$### *$*#***»*!7 k o -3.000 ;*f#*##»# ALL GR30OS COMoI’JfcU SUM OF SQUARES DF MEAN SQUARE F RATIO KcA'I 0.5SL7 BEIRE-lf 195.0732 5 39.0146 2.8935 S T E V 3.7934 UITHIJ 1862.6609 __ 138 13.4975 MAX iMUM 16.0003 ' t o t a l " 2057.7341 143 MNIMLiM -3 .0000 INTCPVAL Series j — ;■ f 1 Z 5 ■p- n 3.uOO )*♦ 00 1.530 )•• $ *$* C .0 -1.‘=j3 ) $ $* » +> -3.COO .-OS -4.503 ) * * $ ►13 -6.00-» 1 • t o -7.530 ) *# $ -OJ ' $ "" ♦ ♦ AS -9.u30 ) ♦ o -1C.530 J — 12.v33 » _ ___ * tH -13.530 » P o — 15•uOO ) $ At * “O KEAM —0.667 -1.917 -5.750 -2,79? -0.875 -3.625 underlined means significantly s rev 2.014 1.316 5.227 2.284 1.393 4.251 different than 0 at .05 level N 24. 24. 2 4 . ______24._____ 24. 24. ALL GROUPS OOMdlNEO SUM OF SQUARES OF MEAN SQUARE F RATIO Ht A'] — 2.t C 4 2 BETWEEN 436.5513 5 87.3102 8.9791 S CtV 3.52o5 WIThIN 1341.8743 138 9.7237 MA X I h u m ' 3.0000 t o t a l 1778.4255 143 MlyIMUM -15.00Ù0 TABLE 19. HISTOGRAMS AND DESCRIPTIVE STATISTICS BY SERIES FOR MALE OF GOOD PHYSICAL FITNESS (TOP) AND SEDENTARY MALE (BOl'TOM). F RATIO TESTS HYPOTHESIS THAT MEANS ARE EQUAL. NOTE: HISTOGRAMS /vRE PRESENTED HORIZONTALLY. INTERVAL Series y — z 3 —4 5 é 9.030 1 “ W 7. 5 jj 1 C 6.«30 ) o 4 . 50 0 I 3.U90 1» -P 1.590 1 65 0.0 )««**• #****$*$* J: -1. 590 ) •• o -3.U90 m -4.590 ) «*«***» -0 -. -A.COO 1 -7.aOu 1 -9.uOO ) #$ o MEAN -? .QA? -?. 792 -l.OCO -0.953 -I.7oa -2.292 undsrlined c:ù:is s ign i i ic2 r. c ly o S DfcV 1.9B1 1 .Jc2 3.121 2.293 1.546 1.939 diCferenc ch.-.r. 0 ac .05 level % N 24. 24. 24. 24. 24. ALL GRJL.OS CCNoINEU SUM OF SQUARES DF MEAN s q u a r e F RATIO ML 49 -1.7 j5f BETr'EE.N 63.3567 5 12.6713 2.7943 _ _ S CEV 2.1953 WI THI.N 625.7903 133 4.5347 MAXIMUM 9.0000 TOTAL 689.1470 ■ 143 ______MINIMUM -3 .0000 INTERVAL Series 3-4 5 é 19.UO" 1 -P-vD 12 .0 0 0 I lO.uOO I B e.ooo I I § - 6.^03 •H 4.')0u $ 2.U00 ** *«4 * (0 0.0 )**• $»*#**##$$ »# -2.009 *$$$ * »** IQ> -4.U00 ) $$ 9) I * 'X3 -9.000 )•* $$$#*# O -n.woo ) 'S' M^AN C.95P 0.750 3.375 -2.833 -1.917 - 0 . 0 4 2 underlined means significantly S f'EV 3.273 3.326 5.037 3.632 1.886 3 .1 2 7 different than 0 at .05 level Q. N 2&. 24. . _ 2 4 . 24. 24. 2 4 . % All_CROyPS COMol .90 SUM OF SQUARES OF MEAN SQUARE F RATIO MEAN U.U406 DEThEEN 589.4377 5 117.8875 9.6423 -______s CEV ______3 .9 9 0 1. WI IKIN 1637.2063 138 12.2261 M*XI“UM 13.0000 TOTAL ' 2276.6440 143 • MINIMUM ■■ -8.0000 TABLE 20. HISTOGRAMS AND DESCRIPTIVE STATISTICS BY SERIES FOR FEMALE OF GOOD PHYSICAL FITNESS (TOP) AND SEDENTARY FEMALE (BOTTOM). F RATIO TESTS HYPOTHESIS THAT MEANS ARE EQUAL. NOTE; HISTOGRAMS ARE PRESENTED HORIZONTALLY. 150 of the underprediction or overprediction for each series. The range of means is considerable for M G , M S and F S . How ever, since the range of means for F G is only 1.8, there appears to be a constant underprediction error of approxi mately 1 to 3 beats/minute. By testing the hypothesis that the means are equal to zero versus they are not, it can be determined whether the underprediction or overprediction is significant for each series. The underlined means of Tables 19 and 20 indi cate a rejection of the above hypothesis. Fourteen of the 24 means must be considered not equal to zero with 12 indi cating an underpredietion and 2 indicating an overpredic tion. Only the mean error for series 5 was significantly different than zero, for all subject categories. Otherwise, there was no apparent underprediction or overprediction for any given series. Since the first task of Series 5 was at zero work load and the third task was of only 20 seconds duration, most of the error for Series 5 can be attributed to the difference in the predicted and observed steady state values for the second task. As can be observed from Figures 4l, 4?, 53, and 5 9 the error at steady state for Task 2 (-1 for MG, — 2 for MS -3 for FG and FS) is on the order of 1 to 3 percent. Since the validation sample is small and the prediction error minimal, this consistent and significant undorprediction for series 5 is not sufficient evidence to recommend that the work load to steady state %RHR relationships 151 bo examined for work loads in the range of task two (35 to 90 watts). There is no consistent trend of means for the other series which indicate an underprediction or overprediction. Also, it can be noticed that overall error means for MS and FS are positive and overpredictions and the overall error means for MS and FG are negative and underpredictions. There is no apparent trend to indicate a mean error of other than zero for predictions for MG and FS, since the hypothesis that the mean equal zero is accepted. However, the underprediction is consistent for MS and FG. The over all subject category means and the means of 9 of the 12 series are significantly different than zero. The valida tion results produced by the MS and FG subjects are definite indications that the work load to steady state %RHR relation ship of MS and FG used exhibit a slight underprediction, for the two subjects tested. Conclusions as to the relative validity of predictions for each subject category can be drawn by examining the over all means and standard deviations of each subject category (see Tables 19 and 20). At one standard deviation the poten tial error of MG, FG, and FS is approximately 4 beats/minute (4 .3 , 4.0, and 4.0, respectively). However, the potential error at one standard deviation for MS is 6.1 beats/minute. The error for MS is 50% greater than that of MG, FG and FS. It can then be concluded that the predicted results for MS are less accurate than those of the other three categories. 152 Phis is due to the underprediction and not necessarily the dispersion of the error since the range and standard devia tion for MS is less than both MG and FS. Analysis by Inspection of Plotted Results Male of Good Physical Fitness The predicted and observed results are plotted in Figures 37 through 42 for the MG subject category. The most apparent source of error is that the observed time to steady state is less than the predicted for all step changes of all series. Therefore, there is an underprediction for step increases and an overprediction for step decreases. Since only two levels of physical fitness were used for this study, varying degrees of physical fitness exist within each level (good or sedentary). The subject for validation testing had a highly developed cardiovascular system (see Appendix 2 for exercise history). Of the total population of persons with in the classification of good physical fitness, subject MG-3 would surely be in the top 3% in physical fitness. Therefore his cardiac response to a step change in exercise was in all cases much faster. For step changes from an increasing or decreasing heart rate the error becomes more pronounced as sliown in Figure 42 at time 20. In this case, the subject's heart rate approached the steady state level of task one more quickly than the model output. Therefore, the observed response was a decrease and the predicted response was an increase. These results certainly indicate the need for more 153 O obsorvod 100. • predict od 9 0 . 80. o o Ç o o «70. 6o - o o o o o 6 g © 50 , 1 , , 1 1 1 30 6o 90 120 150 l8o 210 2 4 0 Time (seconds) Figure 37. Plot of predicted and observed heart rote responses for Series 1— MG. 100 ■ O observed ■ predicted 90 - 80 - O O O OOOOOO £70 oooooooooo Go "''V — I— '— "-T- 30 Go 90 ] 20 150 ](I5 210 2/|0 Timr ( sr(onds ) I'l.m n f 3 M, iMot 100 O obsorvod . predicted 9 0 ooooooooo o :8o 7 0 o 00 o OOOOOQGO O© 1 ' ' I ' ' I ' ' I ' ' I ' ' I ' ' I ' ' I ' ' r 0 30 60 90 120 150 180 210 2 4 0 Time (seconds) Figure 39. Plot of predicted and observed heart rate responses for Series 3-MO. 100 O observed . predicted 90 080 9 o u od ^70 oooooooQ 99 o (»o o O O O O O O © © — r--1 j 1- ' I— ■ j---1 I-- I-- r—— I ^ I — I ■ j 1- ■ -I-- J ■ 1 '■ I-- 1-- 1-- 1-- p— > 30 O o 90 120 1 30 180 210 2 40 r i me ( iM- OJ J» I •- ) ) i.ii'HT lO. P l o t of |u c m I I (■ t oil iiJiii o b s o r v o d Im *.u *L I’m I o rr*) m j m n o s for .Sor i o ' 155 100- o OliMcrviid • Prodlctod 90. 80. OOOOOOOOOOOO ^70 60 C> o O O O O O O O O O , , , r. , r 30 60 90 120 150 180 210 240 Time (seconds) Figure 4l. Plot of predicted and observed heart rate responses for Series 5-MG, lOOn O observed • predicted 90- 80 O & OOOOOOOOOOOO 3?o 60 - o 0 0 6 0 0 A I , r- , . I ' ' I ' ' I ' ' I ' ' I ' ' I ' ' r 0 30 r.O V O 120 150 i H O 210 2^10 T i MK* ( I'l nJt«K ) I i Kur (' ' 12. PI 111 oT priMliclc'il arid (tl>‘-orvi*il hrar I ralo rc^paiiMf-s for Serti’M A-MO. 156 levels of physical fitness. (See recommendations of Chapter VI. ) Sedentary Male The predicted and observed results are plotted in Figures 43 through 48 for the MS category. The observed results for decreasing step changes to a resting state in Figures 4 5 , 4 6 , and 48 are not consistent with the predicted results. Since the predicted and observed heart rate responses coincide for the decreasing step change of Figure 43, the observed deviation from the predicted must be attrib uted to individual variations in cardiac responses. The predicted and observed results were exceedingly close for all other step changes. Female of Good Physical Fitness The predicted and observed results are plotted in Figures 49 through 54 for the FG subject category. By inspec tion of all series for FG, it is readily apparent that an overall addition of 2 beats/minute to the predicted results would greatly improve the accuracy of the prediction. Only 7‘X' of the results were overpredictions. The standard devi ation for the FG category is considerably less than that of the other subject categories. Although there was a slight underprediction, it was consistent for all series, and since the dispersion of error was slight, the predictions could be considered good. 13oT 157 J J O O obsorvod • predict üd O O o o o o • • • • 110 o o 1 00 - 0090 6 g 90-1 o G © 8 o. o 7 0J _ , I . — ^ ' ' I ' — 1 ' ' I ' ' r 3 0 60 9 0 1 2 0 1 5 0 1 8 0 2 1 0 240 Time (seconds) F i g u r e 43 . Plot of predicted and observed heart rata responses for Series 1-FIS. 130Î 120 1 O observed • predicted 110 O G 0 0 0 G G O O . O O 100 O O (0 0 0 0 0 0 0 0 0 K o o = 90 o 80 0 TO: I I I I I I I I I o 30 60 90 120 190 ]80 210 M /|0 T i nil* ( M I'l* olids ) I'igiiri’ 44. Plot o I prodic-(iM[ and ob^oi \ od bo.iiM ï*uli' loi- Sir i os 2-MS. lju 158 o o o o o 120 O obsorvod • prodictod 110 . 0 100 . 01 ak "90 J 80 . 70 T 1— '— — I— — 1— '— T n — " - J 30 90 120 150 180 210 241 Time (seconds) Figure 45. Plot of predicted and observed heart rate responses for Series 5-MS. 130. 120 O observed • predicted 110 100 . OOOOOOOOO «90 J e 80 OOOOOO 1 — '— '— I— " ■ I r - — ■ ■ I'” " I 30 On 90 120 ]50 180 210 240 'I' i til»' ( I >tJ»1 '• ) I I’lttI, III ))i III i 1 I I'll 111 ' ' « ' I ' V « ' 11 111',It I rntc rt'.spim.'.r s I'tir .S»Ti»*H MS, 130 159 120 o observed • predicted 110 100 OOOOOOOOO o «90L 80 O0©OOO©©O0 7 0 r 30 60 90 120 1 5 0 l 9 0 210 2 4 0 Time (seconda) Figure ijy. Plot of predicted and observed heart rate responses for Series 5-MS. 130 1 20 - O observed • predicted 110 100 690 ■] ao J! 6 7fi ) “ r 30 6o 50 120 150 KiO 210 I'lO T I m e ( ^ e e o r u K ) I I ,LL u r I'lol III in i’il i I I id Olid idiit I veil 1 1 ear I role responseo Cor Series fi-MS. 160 1 2 0 * Q olîsorved p r e d i c t e d 110 O O O O O 0 100 o o o o o o o o o 0 90 o o 0 o © © © 8 o - 10 f — I— '— '— I— '— '— I— '— '— I— '— " " i — ' ' ' I ' ' r 30 60 90 120 150 180 210 2'lO Time (seconds) Figure A9. Plot of predicted and observed heart rate responses for Series 1—FG. î 120- O observed p r e d i c t e d 110- 100- OOOOOOOOO q k o |90- ® °0000000 © o 70)1 I I I jj ' ' ] ' ' I ' ' I ' ' ] ' ' I ' ' I --- -— r- O 10 bo 90 12 0 1 50 ] 8 0 2 1 0 2 'iO 'i' i Itll* ( .‘I !•(• Oiul «1 ) ‘‘I, I’ l.il n I I < 1 C«| Mil*! h c a il ra te r» ■ j.i )ii i ,it Sc-iii*.-, 161 120. O obsorvoil . predictod 110 ^ oooooooo o 100 J c 80 ■ O oo © o © © © © " — "— I— '— "—1— — 1— '— — " n — — '— '“T “ G 30 60 90 120 150 i B o 210 2 4 0 Time (seconds) Figure 51. Plot of predicted and observed heart rate responses for Series 3—FG. I ■ 120 j O observed « p r e d i c t e d 110 J 100 . C 9 0 . O O 9 OOOOOOOGOO !)0 . Q ••»•••••• o . o O 0 G 0 0 © © © 7'V I 30 C-O yo 12 0 11 0 1(10 2 1 0 2 'l0 T I tno ( ,Mpc<)nf!.*< ) 1 l.w.uif' i’lu t til j i m l i c l n l vtiul ol p I V ptl hi’n rl r e lp re « p ^ t ui‘ .^prtPM 4— I G . 162 luo . Q obaorvod . predicted 110 . 100 K u =90 ooooooooooo O ...... 80 . © © © © O 0 O O 0 © 70 1 ' 1 ' ' I ' ' I ' ' I ' 1 ' ' 1 ' r 30 6o 90 120 150 . l8o 210 240 Time (seconds) F i g u r e 53* Plot of predicted end observed heart rate responses for Series 5—PG. 120 O observed • predicted 110 100 ooooooooooooooo ^90- o 80- I ' ' I ' ' T ' ' I ' ' I ' ' 1 ' ' I ' ' I ' ' r 0 30 Ü0 yo I'Jo 150 ]f'o 210 2^0 I'i m r ( s o c o t h Im ) I’’ i , Sedentary Female The predicted and observed results are plotted in Figures 55 through 60 for the FS subject category. The most apparent source of error for the FS series is that the heart rate responses to step changes in task intensity exhibit linear trends. There is an example of at least one linear response in each of the six series. For an observed linear response the predictive model ■will overpredict for increas ing step changes and underpredict for decreasing step changes. The predictive model was more accurate for FS than MG, MS or FG in predicting steady state values. The observed and predicted steady state values differed by no more than 3 beat s/minut e. 164 o obaorvod 1 3 0 - • prfMlictoil 120 O O O O 110 0 0 © 1 00 - K<3 1-90 - ËOp I — T — — nr— -"— r 0 30 56o 0 90 120 150 180 210 2 4 0 Time (seconds) Figure 55- Plot of predicted and observed heart rate responses for Series 1-FS. 130- O observed • predicted 120 110. 0 0 0 0 0 JOO ÿ 0 0 0 0 0 0 0 ■90 "Oj, ■ I ‘ ' I —— " I- '—|— “ T ” ’— 30 fiO 90 120 130 I M O 210 2'tO 'I' i iii(> ( V rc n n d '; ) I i y lire ,(i, i’lul ci|‘ fir ('<1 i I <‘i| nn«l (ihsr i vi«| lu'juM rat o if ; {m a s c | o, r i f's Ü— l‘.S, 165 130 . O observed . predicted o G o o © 120 . 110 100 4 t j 0 = 9 0 - 80 OOO ©GGOO 0 3 0 6b 90 120 150 iBO 210 240 Time (seconds) Figure 57, Plot of predicted and observed heart rate responses for Series 3-FS. 130 O observed p r e d i c t e d 120 . 110 o o 100 3 â O O O O O O O k .'-90 J M l ) ) 30 (.0 90 120 190 IMO 210 2'i0 I i iiif' ( 'I I ( '' ) I i y n r (' )H . J’ icii (II p r cmI i i: 1 n ;id ol rr v'fil Im nr I rni<‘ rr-•• pnn m | Scr i i s /, - 1 ' S . 166 130 • o obaorvod predicted 120 110 . ooo o o o o o o 100 O K13 30p OOOO0GGOOO -,—,------j— .— ,------r— ,—,------J— H—------r — '—'— r — — '— r — — '— (— '— '— (— 30 60 90 120 150 180 210 240 Time (seconds) F i g u r e 5 9 . Plot of predicted and observed heart rate responses for Series 5-FS. 130 O observed . predicted 120 1 10 - O O O O O O O 1 0 0 - c: '9^ - O . I O I o'. O O Ô O 30 60 90 120 150 130 210 2'l0 ritlK' ( m p c o u i I.h ) I'ii;ure Oo, IMol u i |ireil i I t imI (uitl olisej'V cd licwil'l rati* la'.pansr'M lo r SrTiCM 0— IS . CHAPTER VI CONCLUSIONS AND RECOMMENDATIONS This chapter contains conclusions which can be drawn from this study, recommendations for continued research, and a brief summary of this investigation. Conclusions The most apparent conclusion that can be drawn from this study is that by translating heart rate to percent of resting heart rate (%RHR), the heart rate patterns which represent the cardiac responses to a given work load will be approximately equivalent for all individuals of a given sub ject category. Based on this finding, it was then possible to develop work load versus steady state %RKR relationships for each of the four subject categories. A data bank of hard data patterns in terms of %RHR were accumulated through experimentation. By using the work load to steady state %RHR relationships and by drawing on the data bank of hard data patterns, a predictive model was developed which can depict an individual's cardiac response in %RHR to a series of varying work loads. The predicted responses in terms of 9oRHR are the same for any given subject category. However, the output in terms of heart rate is unique for each level 1 6 7 168 of resting heart rate. In order for the predictive model to be useful, the only individual input variables required are sex, physical fitness and resting heart rate. It should be noted that the predictive model is computer dependent and requires a minimum of 8K memory; however, most industrial organizations have access to a computer of this size. There are definite advantages in using %RHR as a physiological index. The only individual testing required is to determine an individual's resting heart rate. This is easily accomplished and requires no exercise. The use of %RHR provides a mechanism by which standards can be set for personnel selection and job evaluation by using actual and/or predicted heart rate response to exercise as criteria. Prior to the use of %RHR, the variation in heart rate between individuals made the use of heart rate as a comparative physiological variable difficult. By using %RHR as an index, the cardiac responses of persons of the same subject cate gory can be compared directly and compared to preset stan dards (to be determined in subsequent studies). In the analysis of variance of the empirically derived hard data patterns, the variability in heart rate responses caused by sex and/or by physical fitness had lit tle statistical significance. However, plots of the hard data patterns by subject category indicated that certain trends were evident and that there may very well be a 169 difference in the responses by sex and physical fitness. Statistical verification (reject null hypothesis that means are equal) of these trends would be expected by further data, The previous predictive models of Schilpp, Suggs and Vogt were compared to the predictive model of this study. However, this writer had to refine the previous models before a comparison could be made. The range, magnitude, and direction of step change in work load which could be accommodated by the previous models were vastly limited. Also, none of the previous models made provisions for pre dicting the cardiac response to any series of step changes in work load. In a direct comparison of predicted results for series which could be predicted by the previous models, the results of the predictive model of this study were more accurate, for every series, than the predicted results of any of the previous models. The responses obtained from the predictive model were compared to observed results for all subject categor ies. The findings indicated that the predictive model is accurate in predicting an individual's cardiac response to a series of fixed intensity tasks. The analysis also indicated that there was no accumulative error over time. When using the predictive model to predict heart rate response, 90 percent of the time the error (predicted minus observed) was no greater than 5 percent (for high heart rates) to 10 percent (for low heart rates) of the observed heart rate value. 170 Recommendations for Continued Studies The concepts of using the steady state %RHR to ■work load relationships, predicting heart rate patterns directly from empirical data, and using %RHR as a transfor mation are in the infant stages of research at the conclu sion of this study. There are a myriad of possibilities for extended research. The following discussion is what this author feels would be the logical approach to continued studies. It is recommended that immediate research expand the scope of this study to include the whole of the adult working population. This could be accomplished in stages, with each stage addressing a different human variable. It is suggested that these variables be examined in the follow ing order : 1. physical fitness 2. age 3. sornatotype 4. we igh t 5. sex There are, of course, other human variables which may affect heart rate response to exercise, but it is hypothe sized by this writer that the above listed variables will be the dominant variables and override the effects of others. There were two levels of physical fitness examined 171 for this study. The author of this study interviewed more than 50 potential subjects in order to determine the level of physical fitness. During the interviews, it appeared that it would be possible to categorize subjects into five levels of physical fitness by simply relating their responses to standard questions to previously defined standards. It is suggested that research be conducted to determine the steady state %RHR to work load relationship for each of five categories of physical fitness. The results could then be used to expand the scope of the predictive model to include five levels of physical fitness. The inclusion of three more levels of physical fitness would serve to encompass the whole of the working population with regard to physical fitness and to refine the predicted results of the model. The results could also be used as a submaximal test for physical fitness. It is believed by this author that the age variable has little effect on the cardiac response in %RHR to light exercise. If there is an effect, it is probably a gradual effect, and therefore could be examined for age groups within 10 year spans (e.g., 20-30, 30-40, etc., years of age). It may be possible to reduce the number of groups to two with each having a 20 year span, or, perhaps the age factor could be completely eliminated as being insignificant. Only subjects which were predominantly mesophoric were examined for this study, and, consequently the results 172 reflect cardiac responses for this sornatotype. Technically, there could be as many as 3^3 (7x7x7) different somato- types using the system presented in this study, but real istically there would probably be no more than 30» However, an examination including only the categories of endomorphic, mesomorphic and ectomorphic physiques would probably be sufficient. However, if it is found in subsequent studies that the sornatotype variable is highly significant, then it is recommended that two more categories be included which represent a mixture of (1) endormorphic and meso morphic, and (2) mesomorphic and ectomorphic. The subjects of this study were restricted such that there was only a 15 pound deviation in weight for each category of sex. Further studies should include a greater range of weight classes. Fifteen pound intervals from 90 to 225 pounds would probably suffice. It is recommended that the weight factor be examined independent of sex in order to determine if sex can be eliminated as a variable. It is possible that the variation in heart rate caused by sex could be incorporated in the weight factor. It is the contention of this author that predic tion of cardiac response to exercise can be done with rea sonable accuracy and that the results can be used in the industrial environment for personnel selection, job evalu ation and classification and for many other uses. However, the practicability of such efforts would be severely limited 173 if the classification schemes for each of the variables required extensive individual testing and observation. Therefore, it is recommended that future researchers who wish to conduct followup research be keenly aware of the necessity of simplification of the classification schemes. Future testing which is intended to include a repre sentative cross-section of the adult working population should be set up as a computer based operation. The real time feedback capabilities afforded by the use of computers would be immensely helpful in experiments of this kind. Also, and perhaps more importantly, data could be smoothed and collected in a machine readable format during the test ing sessions. Although the initial set-up time may be con siderable, the marginal cost per subject tested would decrease appreciably as the number of subjects tested increased; however, the cost of manual collection and reduc tion of data would remain the same per subject tested. After studies have been completed to investigate human variables which encompass the entire population, it is then necessary to expand the research to include exer cises for the upper limbs only and whole body. It is hypo thesized by this author that there will be a well-defined relationship between the responses to the exercises of this study and the aforementioned exercises. By developing the relationship between these different types of exercises, the predictive model could be expanded to include jobs 174 frequently found in an industrial environment. The work loads examined during this study were light to moderate and within aerobic capacity. Further research could include work loads which require an anaero bic contribution. A study of this emphasis could incor porate an investigation of whole body fatigue as a variable in an attempt to quantify whole body fatigue using heart rate patterns. Since heart rate is perhaps the physiological variable most easily measured dynamically, it is suggested that an empirical relationship be developed between heart rate and physiological cost of work. This relationship would be established for each subject category. Since the human variables which most affect the physiological cost of work will be incorporated directly or indirectly in a future predictive model, the cost of work patterns as well as heart rate patterns could be produced as output of the predictive model. Summary The purpose of this study was to investigate the feasibility of using hard data patterns, in terms of per cent of resting heart rate, to predict an individual's cardiac response to series of fixed intensity tasks. A predictive model was developed and, allowing for a reason able tolerance in the prediction of heart rate values, verified to be accurate. However, the predictive model 175 accommodates only a segment of the adult working popula tion. Since the logic and methodology of this investiga tion have been shown to be not only feasible, but effec tive, it is recommended that research be continued such that eventually the whole of the working population can be accommodated by the predictive model. BIBLIOGRAPHY Aborff, U .; Elgstrand, K.; Magnus, P.; and Lindoholm, A. "Analysis of Components and Prediction of Energy Expenditure in Manual Task." The International Journal of Production Research, Vol. VI, No. 3 (196Ü), pp. 189- 196. Astrand, P. Work Test with the Bicycle Ergometer. Monark Varberg, Sweden, 1973. ______, and Kaare, R. Textbook of Work Physiology. New York: McGraw-Hill Book Co., 1971. Brouha, Lucien. Physiology in Industry. New York: Perga- mon Pressl 19^0. ______; Smith, P., Jr.; DeLanne, R. ; and Maxfield, M. "Physiological Reactions of Men and Women during Muscular Activity and Recovery in Various Environ ments." Journal of Applied Physiology, Vol. XVI, No. 1 (19"501 pp. 133-140. Chapanis, A. Research Techniques in Human Engineering. Baltimore: John Hopkins Press, 1959. Corlett, E. "Cardiac Arrhythmia as a Field Technique: Some Comments on a Recent Symposium." Ergonomics, Vol. XVI, No. 1 (1973), P. 1. Croney, J. Anthropometries for Designers. New York: Van Nostrand Reinhold Co., 1971. Crow, E . ; Davis, F .; and Maxfield, M. Statistics Manual. New York: Dover Publications, Inc., 196I. Dahl, II., and Spence, D. "Mean Heart Rate Predicted by Task Demand Characteristics," Psychophysiology, Vol. Vll, No. 3 (1971), pp. 369- 376. Datta, S. R., and Ramanathon, N. L. "Energy Expenditure in Work Predicted from Heart Rate and Pulmonary Ventila tion." Journal of Applied Physiology, Vol. XXVI, No. 3 (1969), pp. 297- 302. 176 177 Dixon, W. J. Biomedical Computer Programs. Berkeley: Uni versity of California Press, 1970. I'irth, J’. A. "Psychological Factors Influencing the Rela tionship between Cardiac Arrhythmia and Mental Load." ergonomics , Vol. X\''I , No. 1 ( 1973), pp* 5-l6. Geddes, 1,. A., and Baker, L. E. Principles of Applied Bio medical Instrumentation. New York: John Wiley and Sons, Inc., 1968. Greene, J. Y.; Morris, ¥. H. M.; and Wiebers, J. E, "A Method of Measuring Physiological Cost of Work," Journal of Industrial Engineering, Vol. X, No. 3 ( 1959), pp. iSo-i84. Kalsbeck, -J • W. H. "Do You Believe in Sinus Arrhythmia?" Ergonomics, Vol. XVI, No. 1 (1973), p p . 99-104. LeBlanc, J. "Use of Heart Rate as an Index of Work Output." Journal of Applied Physiology, Vol. X, No. 2 (1957), pp. 275-200. Malmo, R., and Shagass, C. "Variability of Heart Rate in Relation to Age, Sex and Stress." Journal of Applied Physiology, Vol. II (1949), pp. I8l-l84. McCormick, E. J. Human Factors Engineering. New York: McGraw-Hill, 1970. Me is ter, D. Human Factors: Theory and Practice. New York: Wiley-Interscience, 1971. Miller, J., and Freund, J. Probability and Statistics for Engineers. Prentice-Hall, Inc . , I965 • Murrel, K. Human Performance in Industry. Reinhold Pub- lishing Corporation, I965. Narco Bio-Systems. Catalogue. Houston, Texas: Narco Bio- Systems, Inc., 1973. Pearson, E. S., and Hartley, H. 0. Biometrika, Vol. XXXVIII, (1951), pp. 112-130. Purswell, J.; Krenek, R.; and Long, L. "Escape Worthiness of Vehicles for Occupancy Survival and Crashes." Report, DOT contract #FH-11-7512, 1972. Rohmert, W.; Laurig, W.; Philipp, U.; and Luczak, H . "Heart Rate Variability and Work-Load Measurement." Ergo nomics , Vol. XVI, No. 1 (1973). Rolf, J. "Symposium on Heart Rate Variability." Ergonomics. Vol. XVI, No. 1 (1973). 178 Schilpp, R. "A Mathematical Description of the Heart Rate Curve of Response to Exercise— With some Observa tions on the Effects of Smoking." The Research Quart erly, Vol. XX (l95l), pp. 439-4^5. Strong, P. Biophysical Measurements. Beaverton, Oregon: Tekronix, Inc., 1970. Suggs, C. W. "An Analysis of Heart Rate Response to Exer cise." The Research Quarterly, Vol. XXXIX, No. 1 (1967), pp. 195-205. Vogt, J. J. ; Meyer-Schv/ertz, M. Th.; Metz, B. ; and Foehr, R, "Motor, Thermal and Sensory Factors in Heart Rate Variations: A Methodology for Indirect Estimation of Intermittent Muscular and Environmental Heat Loads." Ergonomics, Vol. XVI, No. 1 (1973), pp. 45- 60. Wilder, J. "The Law of Initial Values." Psychomatic Medi cine, Vol. XII (1950), p. 392. APPENDIX 1 INSTRUCTIONS TO SUBJECTS Phase I of Testing You have been selected as a subject to participate in an experiment which is designed to supply data which will serve as the basis for a predictive model. Specifically, the data will be heart rate. Your heart rate will be recorded continuously on this strip chart recorder as you perform phys ical tasks of varying intensity on this bicycle ergometer. Once the experimenter has placed the electrodes on you, please be seated in an upright position with both feet on the floor. There is reading material available if you wish to read. You will be seated for approximately twenty minutes. Please mount the bicycle ergometer and place your hands on the grips. Assume this position each time the exper imenter asks you to mount the bicycle ergometer. For prac tice and familiarization, pedal as if you would a regular bicycle until the speedometer needle is on the second green mark, which indicates a rate of fifty rpm. Maintain this rate for all exercises. Pedal until asked to stop. On the stop signal, be seated. There will be a five minute rest period between each exercise. You can cease exercising now. 179 180 Do you feel comfortable with the bicycle ergometer? (if the response is negative, the subject is allowed to exercise until he or she feels comfortable.) Please be seated (if the response is affirmative). Are there any questions? Phase II of Testing Welcome back to Phase II of testing. This experi mental session will complete your involvement in this exper iment. The procedures will be the same as Phase I of testing. There will be a twenty min^^j rest period prior to exercise, a familiarization with the bicycle ergometer, and then exer cises, separated by a five minute rest period. Are there any questions? Evaluation Phase You have been selected as a subject to participate in an experiment which is designed to supply data which will serve to evaluate the validity of a predictive model. Spe cifically the data will be heart rate. Your heart rate will be recorded continuously on this strip chart recorder as you perform a series of physical tasks of varying intensity on this bicycle ergometer. Once the experimenter has placed the electrodes on you, please be seated in an upright position with both feet on the floor. There is reading material available if you wish to read. You will be seated for approximately twenty minut e s. I8l Please mount the bicycle ergometer and place your hands on the grips. Assume this position each time the experimenter asks you to mount the bicycle ergometer. For practice and familiarization, pedal as you -would a regular bicycle until the speedometer needle is on the second green mark, which indicates a rate of fifty cycles/minute. Main tain this rate for all exercises. Pedal until asked to stop, at which time, simply stop pedaling and remain in position on the bicycle ergometer. Begin pedaling when the experi menter signals begin. Be seated when the experimenter signals to stop and be seated. You can cease exercising now. Do you feel comfortable with the bicycle ergometer? (If the response is negative, the subject is allowed to exercise until he or she feels comfortable.) Please be seated (if the response is affirmative). There will be a fifteen minute rest period between each of six series of exercises. Are there any questions? APPENDIX 2 SUBJECT SUMMARY 1 •H rH 0 w (h (C in %—' 1 0 w IV •H ti V in tn -p -p 0 bO *H fa 0 V in 0 ■H 0) k x : fa (C >, 0 5 X i 0 in -ri in c (C faO bo m (IS 0 k H k S B V la X -p X 0) 0) •H ■ri X I S fa û) 'H ü *H •X 0 H (C rC 'H 0 bO>4 0 OJ H 0 X > (3 X fa OOO ft fa ca < X :s — CO fa < Q fa w 1 MGl G M 23 5'11" 155 2-5-2 180 2 MG 2 G M 20 5' 9" 150 3-5-2 1 8 0 3 MSI S M 24 5' 11" 145 2-4-3 0 4 MS2 S M 20 5'11" 145 2-4-3 0 5 FGl G F 23 5 ' 2" 108 2-5-2 80 6 FG2 G F 25 5 ' 2" 120 3-5-2 120 7 FSl S F 26 5 ' 4" 110 2-5-3 5 8 FS2 S F 23 5 ’5" 112 2-5-3 5 9 MG 3 GM 25 5'11" 155 2- 5-2 90 10 MS 3 S M 30 5'9" 155 3-4-2 0 11 FG3 G F 26 5' 4" 110 3-5-2 60 12 FS3 S F 23 5'5" 110 2- 5-2 0 Phase I , a n d II, Subject s 1-8 Validation Testing— Subjects 9-12 Table of Subject Data. 182 183 Subject Exercise History Two Months Prior to Testing MGl— was an all-around gymnast who actively participated in international competition. He trained seven days/week. MG2— was an all-around gymnast who actively participated in intercollegiate competition. He trained seven days/week. MSI— rode a bicycle short distances a few times each month. MS2— engaged in no muscular activity other than walking short distances. FGl— ran at least one mile/day and exercised while teaching tennis classes. FG2— ran at least two miles/day and exercised while teaching body mechanics classes. FSl— engaged in very light sporadic muscular exercise several times/month. FS2— rode a bicycle short distances a few times each month. MG3— was a sub-four minute miler who actively participated in international competition. He trained seven days/week. MS3— engaged in no muscular activity other than walking short distances. FG3— exercised intensively four days/week and engaged in light exercise three days/week. FS3— engaged in no muscular exercise other than walking short distances. APPENDIX 3 HARD DATA This section contains the data points for all hard data patterns used in the predictive model. The patterns Lire presented by task and then by subject category. 184 rivt MALE f e m a l e T i r E M A L E r-.!' AL ooon ^cr^NTAKt ;D':D biDENfAiLY O Cj u 5) Scn^>!rA?V .jcr soOF 31 0 100 10'' ICL ICO V i u * -7 1V ; !0 100 ICO 1 CO ICC X C 11' 1 U - 20 IÛÜ_ 100 JOG 10 0 20 1 15 1 17 1 1 ■ I 12 30 1ÜO 100 100 100 30 1 1 8 " 12: " 1 2 J 11 5 40 100 100 100 100 4 0 1 2 j 12 : 12 J 1 1 = ^ 50 100 100 100 100 5 0 120 12 120 1?; 00 100 100 100 100 6 C " "12 0 12 y X J 1 2 0 70 lOv 10'^ I 00 10 ! 7 l 12 J 12 - 12. 1 7 . b\.i_ 10Ü 100 100 100 EC 12"' 12. 120 1? ) ' 90 IÔO ICO Too' loo" 90 1 2 u ' 1 2 Ü " ! 2. " " ! ^ . i CO 100 100 luO 100 ICC 12 u 1 2 0 12 0 1 2 0 i 10 iOvJ 100 100 100 1 10 120 12 0 12c 12" 120 100 loo leu 103 1 2 0 12 0 12. 12. 12 . 13C. 100 100 lUO 100 13 0 ■ 12. 12 0 1 2. I 0 0 140 10^ 10 0_ 100 100 14 0 12 0 U 0 12 0 12 0 150 ICC i'oo I no 100 1 5 0 " 120 12 : 12 . 12 0 160 ICO 100 luU 100 1 6 0 12C 12. 12. 1 2 0 170 100 100 100 100 1 7 0 12 0 1 7 0 1 2 0 1 2 0 Hard Da ta---Task A1 Hard Data-- Task A 2 H T [ME h a l e FEMALE TIMEMALE FEMAL 03 GÜOO SEDENTARY GOOD SEDENTARY u U O O S E L c N T A R Y G . Ü L SE ( E iTARYi U1 C 100 100 100 ICO C 1 0 0 10 ^ 1. 0 1C . 10 120 113 116 112 1 0 i2 ) I i5 i . 1 1 10 <0 140 123 127 lie 2 0 .4C 1 2 7 1 36 1 3 7 30 140 132 1 3 4 125 30 151 1 3 3 1 4 5 " 1'3 AO 1^3 138 138 130 4 0 156 1 3 4 1.4 1 54 50 ItO I AO 140 136 5 0 icn Itl I'^o 16. 60 1 40 lA'' 140 138 6 0 1 60 1 Jl 1 c " 1 6 0 70 143 140 140 14 0 70 1 6 . 1 . 0 i . " 1 0 6 u 140 J,40 iTÜ 143 ?u 1 6u 1 u- 1 ' . 14 0 90 ' 140 14 0“ 140"' 140 vC 1 E.u lo"' " 1 CÜ IC G 100 IhO 140 140 140 ICO lo C 1 fcO 1 6. 1 6? 1 10 14„ l43 I4u 14 0 1 10 IL.O 1 6 . 1 (: " 1 5 0 120 i40 140 ItQ 140 12C l o O 16 ; i (. 0 1' 0 130 1 4 J 14? 14G 140 I 30 160 i. o 1 .6 140 140 J4C 140 140 1 4 C 1 60 1 6 " l 6 . I 6C 150 140" 14 o' 14u 14? 1 5 0 1 6u l4 . 16 0 1 6 . 160 140 140 IaO 143 l 6 0 16 . 1 6 . 1 60 K 0 170 140 140 140 140 1 7 0 160 1 . 0 1 6u 16 0 Hard Data--Task A3 Hard Data-- Task A4 T i -’E Ac c 1t-t A1 [ TI c t (r, cr , ;-jTA2r Scl'c «2 - L " y 12 ;■ ! 2 - 12 . !2 . Iv, 1 xS 1 X- X X i 1 3 : " Ix ' 2 c 111 1 ■- 1 1 1 1 . - X . 30 I C c 1:0 1 - 1 3 4 3'- 12- 12- 12w AÛ l o 5 1C'' 10 0 1 0 2 to 12 : 12 : l^'i 10: luO 1C 1 Ol 12- 12 1 t o 101 10- U- 1 GO c. 1- ' 7: 1 0 0 1:. 1 , I J J I.'' 1 0 0 1 1 “ 1 , 13. V - I <1 -1 L - - 70 lO'' iOj I 0" lu: 0 0 U- 1 c. -■ 12 , IOC l O G 10- IcG 10 0 1-0 120 12, 12 i 1 1 0 l O v 10 0 1 0 0 10 ) 1 ' ^ 12C 9 ! 2 J 1 1 2 0 lO'^ r : 1 - 1 3 : Ix - 12- i J ■' 1. w : 10 : 1 - ■ ij'j J 0 XX 4. » 1 ',0 1 0 0 10" 1 - , 1:' 1^ & *0 120 ' ICC lO" 10" 10 j 1 j O 12- Î 2 2 12: l o O l O G IC- 1 — 'J ICO 160 12c 12^ I?" 1 /o i O c 10- IwlO 10 0 1 7 0 12 J 12: .2 ) Hard Data— Task B1 Hard Dater-Task B2 e f m a l f H T U'E M w L E 1 IN'F VA Lc r ” • M t CD Gu"H SFPE*;rA5Y rnpi' S c C F G T A a Y G c ^ ü S f c - " T A R Y 6 f’ ^ r r - CT\ C 1 2 0 12. 123 12 : 1 2 - 1/ 12 10 l . G 12.- 1 3 1 1 3 2 1 : 139 12- - - i > 3- 2C 13- 134 1 X : l3 T r. V It 7 i 3 4 X i: 1 . 30 1 3 5 13fc 140 1 4 0 :0 15c 14' 1 4 7 X 5 1 ‘»c 1 ‘tO It'' It J 1 4 : 4C ’ cc It' 1 9 5 i 5 GO 143 1-x : 14 j It ' 5- 1 Ü- i L 1 X- . f c x4: 14' X - : t ; & X . - i ) . ' , /c 14: 14 , It. 1 ' J / - V , ; ■*. ' 1 4 - t r I', G It- 1- j 14 ■) ■. v_ 1 tr I E " 90 1 4 u It; 11 -J 14 : 9 c 1 5u i w" 1 C J Ir - I AH 13 0 143 14' 143 1 4 3 10 — 16- X t - I ' -■ li e 14: 14 : 1 to 1 4 0 1 iG 16'' X Ü w I (.0 16 J 12 0 14- It- .4 j 11 1-'' : / ' 1 1 c- i 1- 14: i4 : xt^ 1 4 3 13C Ic- 1 -, l.j 16 ' x43 L 4 ' It ' i4 ; i t - i< - 1 1. >: X ■' 2 K - I G U ' 14C 14 J l 4 0 1 4 0 150 1 6 0 I Ü w Ic - 1 16 0 1 4 0 lt'3 1 4 3 1 4 : I C O Ic P 1 o3 i 6- 1 7 u 14- 14 0 I t - 14 3 1 7 0 16 0 1 Ù J 1 6 J Hard Data——Task D 3 Hard D^ta ——Task B^i T I «c ■ ’.II. TIME ^ L t ■ A L ^ G O Q u jr A^Y O u T l bL[C JÎ A-'Y C l9? 1-.- 1 •• : 1/. i " i ; l 3-’ 139 1 J 3 L 3 - L : ' ^ 1 ; 124 12 7 1 1 < 1 3 i ^ 0 1 3/ 1 3C li » 1 2 A l'' 5 1 2 7 30 J. 9 i. A G 1 13 11/ 1 0 2 12 1 A L/ 1 2 5 12- ?(■ 50 ICE l 12 iG l l 14 5G 1 2 2 12 A L''! O L 1 "A 10 / 1 0 ir, Y 1 .T ’ 2 1 IQr /. 1 0.1 i ' i ^ / 7 i c " 12 LG IQ'j 10 ; ____ 1 9C 1 : 3 ' ^ i c. V, 12 ■- IJ- YO ICO 100 L J J ICO •JJ l c 1- 120 i_ ' -> J 100 lu G IGÛ 1 U 0 ICu 1 0 0 12: 12 - 12u 1?" i 10 loO 10 J ij ) ICO 1 10 12 w 12 - 12 , i?] 120 1 0 0 1^: 1 : 0 ICu 12 c 12- 12' i ^ . 1 3 0 IC j lOO i o» J ICO 130 U- 1 T _ l AO I C J l'-'O 1 u 10 J 1 A: 1.1 - l i ' 1 1 5 0 ■ ‘ ICo 10 J 1 w 100 I-C 12^ 12 V 1 0 0 100 100 1 .0 ICC 1 0 0 UC 12 0 1 70 lÜ O 10: Ij O 100 1 /G 12" ■ 12: Hard Data— Task Cl Hard Data— Task C 2 TIME MALE H t IK A L E T IK E 6. AL F F cF •A L c 00 GLiuD SEDENTARY 5 L n E \ G ü u D S £ r _ N T A 5 Y u O O O 5 : ^ = \ T A G Y -vi 0 140 lAv 140 14 3 G . i 4 u 1 4 , 1 4 ) i4:. 10 I4u 14'^ 1 4 J 1 4 0 1C 14 7 14 6 1 43 1 5 2 2 V 1 4 0 140 1 4 3 14 3 2 v 1 5 s 1 6" 1 96 i 5 7 30 ” 14: 140 1 4 0 ^ 1 4 0 3Û 1 Ük/ 1 5 5 lu- 1 ' 4 0 l4j 14"' 1 4 0 14 0 4 0 16 3 1*^0 1 6 - u- : 50 1 40 14"' 14 0 14G 5 0 1 6 0 lu'l 1 6 - 17.- 6 0 1 4 0 14 0 l4 0 14 3 67' 1 6 : 1 (.■ : I — - 70 140 1 4-^ ! 4 V 140 70 17 - 1 ^ 1 B u ______1 4 0 ______1',: 140 140 c G i/o 1 o : T. : 1 7- 1 S)0 1 4U ' l40' 1 4 0 " 1 4 0 90 1 6 u ’ l c 5 1 eu 1 0 U 1 0 0 14 0 140 1 4 3 14 3 ICO KG 16 V i 6 - U; : 1 iC lAO 14 J 14 0 140 1 1 0 IcT 1 - L i 6 : 16: 12 C 140 14 J 140 14 0 1 2 u i (. 0 16" 17 : u : 13 0 I4 u 1 4" 1 4 0 1 4 0 1 3 0 l tZ 1 6- : 1 e- U.r 1 4 0 14 3 1 4 0 140 14 3 1 4 0 UT l o - U-: 17- , 1 50 140 140 i tC 14 : 1 50 le- 1 6 : le — 16 3 1 6 0 140 140 140 1 4 0 1 6 u loO 1 6 0 u: 1 6 : 170 l 4 0 143 1 4 u l-.v 1 7v 1 6 0 I c C 1 to 1 6 - Hard Data— Task €3 Hard Data- -Task C4 T I K E - MALE FEMALE II ’-•E ,'l -A L c r V * Al. r. GÜÜÛ S cl r NT -,7 Y G j O L SE HE -iTARY c u u u r.^ L .NT.'K Y J o ^ S E ' E .1 0 It. 1 0" 1... K 3 0 1 ' : 1 - : IG I h . iDv 1 5 2 K. & 1 1 3 d I D. 1 34 14 J 1 - > Î '• ■ ■; - > ' ‘ 3C 123 ^ 1 2 d 132 132 3 0 K. 14 4 i D ■' 1 D ' 4 0 1 15 li.9 1 2c 123 4 0 1 35 K l 1 Sx. 144 50 1 10 1 15 1 12 1 14 5 0 125 i 3^ 12 7 X 37 t o 1 0 5 1 1 1 I"? K ) to I 2*, 1 3-. 1 2 4 1 3-' 10 102 1C t. 1 j O IC'D 7v Ir 3 1 3 4 i ;k x’ ' K 7 PC KO 107 i -J J K 2 5. 122 i J - 2 i 00 IOC K D 1.3 100 9C 12 1 X 3. lO .3 12- 177 ICOIOC K 3 KOICO ICC 120 12L 12 J n o lOo 100 130 lOu ) 10 120 12 5 12 3 12 1 120 iCv 10. 100 lOO 12: 1. J C 12 •. 1 2 . 17 _ loC ic: I or K J 10 J 1 d O 1 2 J 12 1 4 - i ? - 140 IOC K G K 3 ICO i^C KC 12 - 12 :■ 1 7 3 i ÔU 10. ' lOO' ' 'ICO ICO ... 150 120 i Z V x2 3 1.7 7 IfcO 100 103 lu3 100 160 120 i?: 125 12 3 I IC 100 ir n KO 100 170 KC 12 1 12 3 12 0 Hard Data---Task 01 H a r d Data — Task 02 - - H T I ^ E K.ALc E l 2. AL E UNE K..\L E Fuf•■ALE 00 G ü C u oECENTARY Gnpu S c L ' c i r A R Y G U ^ u 5 c p r M T ri Y C ~ P L S u . T O I \Y 00 u 16 0 l ù 3 K O 16 0 160 1 3 1 D K . 10 K 5 154 1 5 4 KO 1C I K 1 u : : ' : 20 1 50 151 14 9 1 5 6 c C K C K " 1 It. 30 1 44 K 3 145 K 4 30 1 6 6 KO 1 60 1 6 : 4 0 141 K 6 1 4 ? 1 5 2 4 0 16 3 l o C lu. 16 7 50 1 4 5 1 4 4 l41 KC 50 K u K 6 i t : K C 5 0 1 4 U 143 ' 40 14 0 ( C l. K K •/ K.3 1; . •KO 7 0 K v K c i 4 0 14 7 K lu" 1 6^ 1 < : J u 14 3 K J 1 Au 14 6 K . K . 1:-J it y 50 14,^ ItC ' 1 ,3 1 4 4 50 16: K O 1/ : ; f G 1 3 0 K O K O 14 3 1 4 2 1 0 0 l (■ 3 1 60 K-c KO l i n 14C 14. K O 14 3 1 1 0 1 tc I r K 1 6/7 1 tu 120 140 14 . K^ i 14 5 K : 160 i . . 1- ; 1' 3 13C 1-.: K 3 1 A 3 KO 1 sn K'- 1 6^. xc 3 1 4 0 140 K 3 1 4 3 KC 140 K C K u 1 u x5 C 14C 14 J K u KO 1 5 u 1 6C 1 rK K : 16. I t O 140 14'7 1 4 0 KC I b O 1 60 1 60 1 u . 11 0 1 7 0 140 140 1 a O 14 0 1 7 0 KOKO 1 6 . K 3 H a r d D a ta — — T a s k D 3 H a r d Da ta --Task D4 APPENDIX 4 ANALYSIS OK VARIANCE TABLES FOR ANALYSIS OF HARD DATA PATTERNS The following twelve analysis of variance tables are for analysis of the data collected for the twelve hard data patterns. They are presented by the two character codes where the first character is alpha and refers to the initial value, and the second character is numeric and refers to the steady state value. A, B, C, and D are ini tial values of 100, 120, l40,and l60 %RHR, respectively. Digits 1, 2, 3, and 4 are steady state values of 100, 120, l40, and l60 %RHR, respectively. The sources of variation are numbered and refer to the following main effects or interactions ; 1 mean 2 sex (S ) 3 physical fitness (P) 4 time (T) 3 SI’ 6 ST 7 PT 8 subjects (V) 9 S PT 10 VT 11 error. Tlie indices i, j, k, 1, and m are the same as those pre sented in the mathematical model in Chapter IV. A symbol 189 190 to 1!>(! Lof t of (lie numbered source of variation indicates tlie level of significance, if any. The symbols are as follows : O - .10 level □ = .05 level /\ = .01 level /TASK AZ\ ST l RCE tPR''R TER-' F SUM n SQUARES DEO. OF MEAN SQUARE EXPECTED MEAN SQUARE FREEDOM I KEAN 'IIJK) 1931173. 1 1931173. 144.000 I 1 ) IB.OO/JI 3) 2 J I ( jK 1 0 , 2 5uR 1 6 . COGOO 1 1 6 . QOOOO 72.000 1 2 ) 18.0001 8) 3 K I( JK) 0.1114 7.111111 1 7.111111 72.0 0 0 1 3) 18.0001 3) 741.1606 16.0001 4 ) 2.000110) A'' L i L (JK) 30.3164 5929.287 8 5 JK 11 IK ; 1 . 7o3E 117. /77b 1 113.7778 36.0001 5) 18.0001 3) 6 J l IL ( JK) 0 . ’ 754 29. 5 1 5 0 3 8 3 ,689453 8.000 I 6) 2.000110) 7 KL I L (JK) ' 0 . 2 8 3 b 3^.40234 8 3.800293 8.000 1 7) 2.000110) B lIJKI 255 , 2 2 2 0 4 6 3 . 8 0 5 5 0 18.000 I 8) 9 JK.L IL(JK) 1.347S 144.4332 8 18.05414 4.0001 9) 2.000110) 10 1 1 (IK) 4 2 8.7385 32 13.39308 2.0901101 11 M( I Ji-L ) 2 3 3 . 3 1 2 5 72 3 .247396 l.OOC 111) - - ■ — /TASK A 3 \ SO,..RCt EO)^^ ^ERP 1 SUM OF SQUARES DEC. CF MEAN SQUARE EXPECTED MEAN SQUARE FREEDOM 1 K E A N I(JK) *** $ * » » * 2426325. 1 2426325. 144.000 I 1 ) 18.0001 8) □ E J 1 ( J k ) 1 9 . 0 6 j 7 220.0273 1 220.0278 72.0001 2 ) 13.0001 8) A 3 K 1 ( JK ) 44.3149 513.7776 1 5 13.7'. ,5 72. 0 0 0 1 3) 13.0001 8) A " L ILIJK) R23.° 737 2465 1.23 8 308 1.4.0 16.000 1 4 ) 2.000110) H 5 JK IIJK) w . 54 1 3 6 . 2 5 0 0 0 0 1 6.25CC00 36.0001 5) 13.0001 81 \D □ A JL IIIJK) 2.9422 22 3 . 9 3 7 5 a 27.99219 8.0001 6) 2.000110) H A T KL ILIJK) 7.1630 5 4 5.1953 8 6 8 .14941 8.000! 7) 2.000110) 8 IIJK) 4 6 . 1 6 6 7 5 4 11.54169 18.000 I 8 ) 9 JKL ILlJK) 0.9383 7 1 . 4 1 4 0 6 8 8 . 9 2 6 7 5 8 4.0001 9) 2.000(10) 10 I L ( K ) 30 4.4504 32 9.514076 2.000110) 11 K(IJKL) 9 71-5703 72 13.49403 1.000(11) TER^ SUM OF SQUARES DEC. OF KEAN SQUARE EXPECTED MEAN SQUARE FREEDOM 1 KEAN IIJK) 2926949. 1 2926949. 144.0001 1 ) 18.000 1 B! 2 J 1 I JK) 3.9178 17 3.3611 1 173.3611 72.0001 2) 18.0001 8) A 3 K IIJK) 2 3 . 3P29 1034.694 1 10 34.694 72.0001 3 ) 13.0001 8) A" L iL 1JK) 716.3530 55142.41 8 6892.301 16.000 I 4 ) 2.0 00110) D 5 JK 1 1 jK) 15.4 733 6 c; 4 • 6 9 K 3 1 684.694 3 36.0001 5) 18.0001 8) JL 11 1 jK ) . o 7 J 8 3 74.9375 e 46.36719 6.0001 6) 2.000110) OT KL ILIJK) 8 .5202 655.8355 8 81.98193 8 . 0 0 0 1 7 ) 2.000110) 6 U JK ) 177.000^ 4 44.25000 18.000 I 8 ) A 9 JKL IL UK ) 3.7247 4 4 u.6 689 3 55.08362 4.000 I 9 ) 2.000( 1 0 10 ILIJK) Jo 7.906 3 32 9.622070 2 .cool 10) 11 Ml I JKL ) 1099.238 72 15.26720 I.000 11 ) ZlASK 81 \ EP0:q TERM F SCK OF SCUARES OEG. OF MEAN SQUARE EXPECTED MEAN SQUARE FREEDOM 1 mE A" IIJK) ******)** 160/612. 1 160/612. 144.COG I 1 ) 16.0001 8) 2 J I 1 J M L*uOv9 .b?3C!CCC£-01 1 .6250000E-01 72.0001 2) 18.000 1 S) 3 K » 1 J K J I.A33 1 95.0625 0 1 95.06250 72.000 I 3) 13.0001 3) L i n IK ) 7 7.1J14 70'»9. 125 8 RBI.1406 16-0001 4) 2.00 0 '.10) 5 JK lIjKl u.u203 41.17360 1 41. 17360 36.0001 5) IS.00:1 8) 6 JL ILIJK) r.jjci 27.25781 P 3.407227 8.003 1 6) 2.000 110) 7 KL ILIJK) 1.23 33 169.7578 8 13.71973 8.000( 7 I 2.000110) e KJM 265.5273 4 66.3 8184 18.0001 8 ) 9 JKL .( IJKI 1.j 023 97. 11937 a 12.13992 4.0001 9 I 2.000110) 1C ILIJK) 365.7068 32 11.42834 2.000110) I i M Ur u ) 359,2186 72 4.989149 l.OOOI 1 1 ) /TASK (33 \ SC k '-E EKrt_,'. TERW F Su m OF SQUARES DEC. OF MEAN SQUARE EXPECTED MEA N SQUARE FREEDOM 1 MEAN IIJK) 2o59344. 1 2659344. 144.0001 1 ) 1 8.C 0 0 1 6) 2 J 1 1 Jk) ...28 72 93.06250 1 9 5 . 0 6 2 ;o 72-000 I 2) 18.000 1 8) 3 K 11 IK) C. 1044 4.340278 1 4.3402'8 72.0001 3) 18.0001 8) A " 1 ILIUKI 3C.234J 61 72.4 04 8 771.5605 16.000 I 4 ) 2.00:110) 5 JK IIJK) J .204 7 8 . 5C6936 1 8.506 936 36.0001 5) 1.9. : 0 J1 ? ) \D ro 6 JL ILIJK) 1.5443 189.7578 8 23.719 73 3.0001 6 ) 2.030 1 1C) 7 ^L ILI JK ) J.3070 37.72656 8 4.715820 8.0001 7) 2.0001 10 I e 11 JK ) 166.2499 4 41.56248 18.0001 8 ) 9 JKL ILIJK) C .230? 20.28604 8 3.535755 4.000 I 9> 2.000110) 1Ü ILIJK) 49 1.4950 32 15.35925 2.000(10) 11 M I J" L ) 115.2344 72 1.600477 l.COOl 11) /TASK B4\ SC . - ‘■.L tkKul T L R M F SUM OF SQUARES OEG. OF MEAN SQUARE EXPECTE Ü ME. SQUARE FREEDOM 1 7 BAN 1 1 JK 1 316335F. 1 316 3358. 144.000 I 1 ) IE.0:01 6) 2 J 1 1 JM C . 447 5 31. 17 360 1 31. 1 7 360 72.000 I 2 ) 18.0001 8) 3 K 1 1 JK ) 3.4119 237.6736 1 237.67 36 72.0001 3) 13.0001 8) 4) 2.000 110) A ' - i iL 1 JK ) 25126.23 a 3240.702 16.000 { □ 3 JK I IJKI _.07 JO 634.3393 I 604.3398 36.000 I 5) 13.0001 a ) 6 JL :l ( IK ) 0.68 77 (0.693 31 a 8.836(14 a.cco I 6 ) 2 . 0 0 0 1 iC) 7 Kl i L l J K ) K.3853 245.2031 8 30.65039 3.0001 7 ) 2.000110) a IIJK) 278.6387 4 6 9 . 6 5 )67 18.000( 8 ) ^ 9 JKL ILIJK) 3.77^1 593.5731 8 74.19727 4.000 I 9) 2.000110) 1Ü ILIJK) 4 11.1^73 32 12.84991 2.000110) 11 M ! Jr L ) 1J29.078 72 14.292 75 l.OOOI 11) - /TASK Cl \ SCi.-'Cfc e r R vja t e r m F S'uM OF S t U A R E ‘0 DSG- CF MEAN SQUARE EXPECTED MEAN SQUARE FREEDOM l MEAN K J M 195 î 7l 4. 1 1953704. 144.000( 1 ) I 8 . 0 0 C ( 8 ) 2 J I ( JK) 0.3343 73.37300 1 73.67360 72.000( 2 ) 13.0C3( 8; 0 3 K l ( JK) 7.3392 1566.840 l 1 566. 340 72.000( 3) 18.033( 8) A " >- IL(IK) 220.3363 24537.73 8 3067.216 16-0001 4) 2.033110 1 3 JK l ( J k ) 2.3821 495.0623 1 495.0623 36.000( 5) 18.030, 8) t JL IL(JK) 1.P143 201.8372 e 25.2 3340 8.000 1 6) 2.C O O (10) A 7 kl ILIJKI 3.77JI 641.9414 8 80.24268 8.000 t 7) 2.000(10) 6 1 (JK ) 831.3057 4 207.8264 18.0001 8 ) □ 9 JKL I L (J K ) 3.6573 4 U 6 . 9 4 17 a 50.86771 4.000( 9 ) 2.000110) 1C I L (JK ) 445.014 6 32 13.90671 2.000(10) 11 MIIJKLI 2979.039 72 4 1.37553 1 . 0 0 0 (111 - ■ ■ /TASK CZ\ SCARCE F R R C ’ TERM c SLM OF SCOARE S DES. CF MEAN SUUARE EXPECTED MEAN SQUARE FREEDOM 1 MEAN I ( JK ) ******** 232 1 C50- 1 232 1050. 144-000( 1 } 18.0001 8 : 2 J IIJKI 0.9769 93.44444 1 93.4444 72.000( 2 ) 18.030 ( 8) 3 K I ( J K ) C .2 614 25.00000 1 25.00000 72.000( 3) 18.000( 6) A'- L IL(o K ) 7 o . 0 8 6 9 6*91.234 d 861.4043 16.000( 4 ) 2.000110) 3 JK I l jK ) C .0003 -27 '71CGE-01 1 .2 7771035-01 36.003 ( 5) 15.00u( 8) 6 JL IL(JK) C . 8027 8 5. J1230 8 10.72656 8.000 1 6 ) 2.000 1101 7 KL IL ( JK ) 0.6807 37.00781 8 4.625977 8.G30( 7) 2.000110) S I(JK) 382.6108 4 95.65271 18-000( 8 ) 9 JKL IL(JK) 0.2953 PP.70270 8 3.587837 4.000( 9) 2.000110) IC IL(jK) 388.8577 • 32 12. 15180 2-000( 10) Il M ( I JK L i 516-7656 72 7. 177299 1 - 0 0 0 (111 C * \ /TASK EXPECTED MEAN SQUARE SLi. PCt ERT^a TEPM F SUM UF SQUARES CEG. OF MEAN SQUARE FREEDOM 144-000( 1 ) 13.0301 3) 1 MEAN I t JK ) ******** 3483488. 1 34 3 84 88. 68.06250 72.000( 2 ) 1 B . 0 0 0 ( 3 ) Q 2 J KJKI 6.6719 68.06250 I 9.506944 72.COO( 3) 13.0031 8) 3 K I(jK) C .93 19 9.506944 I 16.000( 4 ) 2.030110) /\4 L ILtJK) 154.I73E 6337.352 0 792.1689 33.06248 36.r>C0( 5 ) 18,030( 81 5 JK I ( Jk 1 3.2410 33.06248 I 13-79 )32 a.ooot 6) 2 . 0 3 C I 10) 6 JL 1 L ( JK ) 2.6857 110.3945 3 8 - O C O ( 7 ) 2 .000(10) 7 KL ILtjK) 0.6137 33.44922 8 4.12 1152 18.*00( 8) fc I {JK ) 40-80556 4 10.20139 4.000( 9 ) 2.003(10) 9 JKL IL(JK) 1.1272 46.33205 8 5-791506 2.000( 10) 10 IL'JK) 164.4210 32 5. 138156 1.000( i n Il M(IJKL) 533.2690 72 7.406514 /fJTf! d A SLR RLE E R R O R TERM. F SUM OF SQUARES DE C. UF MEAN SQUARE EXPECTED ME AN SQ UA R E F R E c C C M I MEAN KJKJ 2 1 9 H C 5 3 . 1 2 1 9 8 0 5 3 . 1 4 4 . 0 0 0 I 1 ) 18 .0001 8) 2 J I( JK ) Ù.K345 IR. )62 5J 1 1 6 . 0 6 2 5 0 7 2 . 0 0 0 ( 2 ) 1 8.0 0 0 1 S) 3 K I ( Jk ) 1 . 6 8 5 6 90 7. 00 6 8 1 9 8 7 . 0 0 6 8 7 2 . 0 0 0 I 3) 1 8.G0 0I 8) A** I. IL(.K) 1 9 5 . 7 4 2 2 5694 1.45 E 7 1 1 7 . 6 8 0 1 6 . 0 0 0 1 4 ) 5 JK 2.000110) KJKI C . I 300 6 E . 0 6 2 5 0 1 6 8 . 0 6 2 5 0 3 6 . 0 0 0 1 5) 1 8 . 0 0 0 1 3) 6 J L I L (JK ) 0.OP91 24 1. 1 0 3 6 8 3 0 - 1 4 7 9 5 8.0001 6 ) 2.400110) 7 KL i L (J K ) 1.Ù4 5G 3 L 3 .9961 8 3 7 . 9 9 9 5 1 8.0001 7 ) 2 . GOO ; 10) 5 1 (Jr ) 2 L 9 3 . P G 6 4 5 2 3 . 4 5 1 4 1 8 . 0 0 0 I 8 ) 9 JKL ILIJK) C . 52Ü6 1 5 1 . 4 5 7 0 8 1 8 . 9 3 2 1 3 4 . 0 0 0 1 9) 2 . 0 0 0 1 1 0 ) IG I L ( Ir ) 116 3.601 32 3 6 . 3 6 2 5 2 2 . 00 0 ( 10) 1 I I I J- L ) 2 3 3 ^ . 4 9 2 72 3 3 . 0 9 0 1 6 l.OOO I 11) /TASK D 2 \ scTtuTt i.R^rn •EK" SUM or SOUAtiES CEG. CF KEAN SQUARE EXPECTED MEAN SQUARE F R E E C u K 1 MEANIIJK) 2 P 0 6 4 6 2 . 1 2806462. 144.000 I 1 I 1 8 . 0 0 0 1 6) 2 J I 1 JK) C . O 0 6 9 5 . 8 4 0 2 78 1 5 . 8 4 C 2 7 8 7 2 . 3 0 3 1 2) 18. 0 0 0 1 8) 3 K IIJK) 2 . 1 9 8 6 1 6 5 6 . I 74 1 1856. 1 '4 72.000 I 3 ) 18.0001 8) A" L ILIJK) 6 2 . c I 4 V 1 9 1 6 3 . 4 3 a 2 3 9 5 . 4 5 1 6.0 0 0 ( 4 ) 2 . 0 0 0 ( 1 0 ) 5 JK I 1 jK ) 0.^513 4 3.340Q9 1 4 3 . 3 4 0 0 9 3 6 . 0 0 0 1 5) 1 8 . 0 0 0 1 6) 6 JL lllJK) 0 . 71 3 1 2 2 1.25 70 8 27.65088 8.003 1 6 ) 2.OGGI 10) \D 7 KL ILIJK)" 1 . 0 2 7 9 3 1 6 . 6 1 7 2 8 39. 5771 5 8 . 0 0 0 1 7) 2 . 0 0 0 1 10) 8 I 1 JK ) 3 3 7 6 . 6 R 6 4 8 4 4 . 1 7 1 4 1 8 . 0 0 0 I e ) 9 JKL IL (JK) 0.8032 247.4138 8 30.92673 4.0001 9) 2 . 0 0 0 1 1 0 ) 10 IL 1 jK ) 1 2 3 2 . 1 0 0 32 38.50311 2.000(10) 1 1 MI I JKL) 16fcl. 125 72 23.34895 l.OOOI11) /TASK 03 \ SCARCE Ei\ 1 MEANIIJKI 3 1 5 2 1 0 3 . I 3 1 5 2 1 0 3 . 1 4 4 . 0 0 0 1 1 ) 18.0001 a I 2 J IIJK) Û• 9665 264.0625 1 2 6 4 . 0 6 2 5 7 2 . 0 0 0 ( 2) 1 8.00 01 bi 3 K IIJK) 2.0425 779.3401 1 7 7 9 . 3 4 0 1 72.0.90 ( 3) 1 3.00 01 8) 4 I A'* L IL U K ) 57.114) 5 145.465 3 643.1831 16.000 1 2 . 0 G 0 I 10) 5 JK IIJK) C.9468 2 5 8 . 6 7 3 6 I 2 5 8 . 6 7 3 6 3 6 . 0 0 0 1 5) 13 .G 0GI L) 6 JL ILIJK) 0 . 6 5 2 2 5 E . 75391 8 7 . 3 4 4 2 3 0 8 . 0 0 0 1 6) 2 . G 0 0 I 10) 29.37109 8.000( 7) 2 . 0 0 0 ( 1 0 ) O 7 KLILIJK) 2 . o08 I 234.9,sag 8 e I U K ) 1 0 92 .86 1 4 2 7 3 . 2 1 5 3 1 8 . 0 0 0 I 8) 9 JKL ILIJK) 0.3)54 35.61938 8 4 . 4 5 2 4 2 3 4 . 0 G 0 ( 9 ) 2 . 0 0 0 1 1 0 ) IG ILIJK ) 3 6 0 , 3 6 1 3 32 11.26129 2.000(10) 1 1 Ml I JKL ) 2 2 0 . 2 4 2 2 72 3.C50919 1.000(11) APPENDIX 5 ERROR DATA This section presents the validation data in terms of beats/minute error (predicted minus observed) at 10, 20, 30, . . . 240 seconds for each of the six series of exercises performed by a subject in each of the four subject categories The data are presented by subject category. The large script numbers (1-6) are series. The small script numbers are time in seconds. 195 Time (seconds) ^ 3 . 0 10 7 3 . 0 3 0 0 0 ^ 2 . 0 0 0 0 0 ^ -0 .0 / - 3 . Cj CC0 - 7 . 0 0 3 0 0 3.0 J- C .0 - .0 - 0 . 0 J. - ‘t . C j w j O — -? .0 0 :0 0 0 . 0 1 .0 0- 0 0 -1 .0 3 0 0 0 " - 0 . 0 - 4 . 3 0 3 C J - 2 . 0 3 0 0 0 0 . 0 -2.-0,300 - 5 . 0 0 0 0 0 -0 .0 - 6 . 0 C C C Ù j.C O O C C — . 0 -1 .- 3 3 3 0 - 7 . O 0 C G 0 -0 .J - c . 0 : 3 0 0 4 . 0 0 0 0 3 - .3 60 - 1 . 0 0 0 0 0 — 5. - 0 0 G - . - - I . o o c c o 4 . „ ^ o 0 -, 0 . 0 -1 .3 00 0 0 - 3 . 0 0 0 0 0 - 0 . 3 - i . 3 '' 3 0 0 4 . c : u o c 0 . 0 — 1 .-- — 03 - 2 . 0 0 0 0 0 - 0 . 0 - 1 . C C1 0 0 4 . 0 : 0 0 3 3 . 0 -2 .03000 — 2 . 0 0 0 0 — -0 .3 - 3 . 0 C C C U 4 . 0 0 : 3 3 3 .0 -2 .0 -0 0 0 — 2 .-0- 0 - - 0 . 0 - 3 .3 0 G C Ü 4 .- . 0 3 0 0 - 4 . 0 0 0 0 0 - 3 . 3 3 0 0 0 - 2 . 0 0 0 0 0 1 .0 00 0 0 - 1 . 0 3 3 0 0 7 . 0 0 3 0 0 - 6 . 0 0 0 0 0 IZO - 2 . 0 0 - 0 - - 0 . 0 — 3 .0 0 . V 6 . 0 : 3 0 0 - 3 . 3 0 - 0 0 - 2 . 3 0 - " " - 5 . - 3 0 0 3 1 .3 3000 0 .u 12 .0300-1 —2 .3 0 0 00 - 2 . 0 - 0 0 0 — 1 2 . - 3 - 0 0 u _ - 3 . 0 1 1 . 3 3 - 0 0 - 1 . 0 0 0 0 0 ' — iC . 3 3o03 - 1 5 . 0 0 0 0 0 - 2 . - 0 0 0 0 V # ^ b . 0 3 0 0 0 - 1 . 0 0 0 0 0 - 5 . 0 0 0 0 3 - 1 5 . 0 0 0 0 0 - 2 . 3 0 0 0 0 0 .0 6 . 0 - 0 0 0 - 1 . 0 0 0 0 0 - 3 . 0 Û C 0 0 - 1 5 . 0 0 0 0 3 — 2 . 0 0 0 3 3 0 . J 3 . 3 3 0 0 3 - 2 . 0 0 0 0 0 - 1 . 3 0 0 0 0 iBO 0 .0 -i 3. 3 3 0 0 " 1 6 . 3 3 0 0 0 1 . : : - 0 3 — 1 . 0 0 0 0 0 1 . 0 0 : 0 0 -11 .00 — 00 — 2 .3 J —00 12 . 3 3 0 0 0 3 .0 - 1 . 0 0 0 0 0 - . - — V . — — — 00 — 2 .3 — 000 Ü . 0 0 0 0 0 3 . 0 -1 .00000 " 2 .000 0 0 -7 .0 30 0 0 - 2 . 0 0 0 0 0 3 . 0 3 0 0 0 0 . 0 - 4 - 2 . 0 - 0 0 0 - 1 . 0 0 0 0 0 3 .000 0 0 .00303 1 .3 0 o 0 0 J . 0 -1 . 0 0 0 0 0 -3 .000 00 - 2 . 0 0 - 0 - 3 . 0 C .0 2 . 0 0 0 0 3 - 1 . 0 0 3 0 0 7^0 1 .3 30 0 0 — ^ .3-00- - 5 . J - 3 0 3 3 . 3 0 . 3 y 2 . —' C 0 0 — H / —2.30 00 3 lb O - 3 . 3 0 0 0 0 A - 2 . 0 - - 0 - /O -l .03300 A J-c A -6.3-000 ___ 3 ^ -1 .3 - 0 0 0 A 2 . 0 - 0 0 0 ____ / ^ - l .00030 / - 4 . - C O C O / - 3 . J '3 C C 0 1 - 0 . 0 t-/-3 .0 - 4 . L C O 0 0 " C -3 .30-0- L _ -‘t.30000 1 4 . 0 0 0 0 0 - 4 . 3 0 0 0 0 - 2 . 0 0 0 0 0 -1 .3 03 0 0 -3 .0000 - - 6 . 3 0 0 ^ 0 5 . 0 C 0 0 0 - 4 . - 0 0 0 0 - 1 . 0 0 0 0 3 -2 .0030 0 - 6 . 0 - 0 0 0 - 5 . 0 0 0 0 3 13 . 0 0 0 0 0 - 4 . 3 0 0 0 0 ___ 3 . 3 _____ ko - 1 . 0 0 0 0 0 -7 .0-3 3 0 - 3 . 0 0 0 0 3 1 0 . 3 3 J " 0 -3 .0 00 0 0 - 4 . 3 0 0 0 0 0 . 0 3 .3 - ^ . O u O O n 6 . — 30 0 — - 4 . 3 0 0 0 0 0 . 0 - 4 . 0 0 0 0 0 - Z . C O v C O 5.00-00 - 4 . - 0 0 0 3 3 .0 ” -0 .0 - 3 . 0 C 0 C U —2 . 3 0 0 0 ^ 2 . 3 3 - 0 " - 2 . 0 0 0 0 0 - 4 . 0 0 0 0 0 3 . 3 - 3 . 0 —2 . v J ^ C O 1 . 3 3 3 3 0 - 4 . 3 3 - 0 3 3 - 0 — - . 0 - l . C - C O O - 2 . J u 3 ^ ^ o . 0 — 4 .- 00 — 0 0 . — —J . 0 - 3 . 0 — 2 . 0 k, V. C u 0 . 3 — 4 . — C — — 3 3 . 0 -2 .OOo O O — - . 0 . 0 0 3 0 0 3 . 3 .0 — 4 . — 0 — 00 3 . 3 - 2 . 0 G O O O -3 3 . 3 0 0 0 3 3 .0 - 4 .-0 300 3 . 0 -3.30000' ■■ - 3 .0 5 . 3 0 0 0 3 - 6 . 0 0 0 0 0 -4,00000 3 . 0 -2.00G0O - 5 . 0 0 0 0 0 4 . 0 0 3 0 3 - 3 . 0 0 0 0 0 -0 .- CC O Û 1 .-o O O O — 2 .0-000 - 3 . 0 3 3 0 0 3 . 0 3 0 0 0 - 2 . 3 3 3 3 0 - 1 5 . - 3 0 0 3 - . 3 0 0 " " /fio — 3 . -0-0 0 - 3 . C 3 C O O 3 .uCCCO - i . 3 0 3 3 0 -li .30330 4 . — 0 0 C 0 -3.3 3 0 0 0 — 3 . 0 - - 0 C 3 . 3 0 3 3 0 -1 . 0 0 3 0 0 -7 .O O O O O 4 . 0 0 0 0 0 ______- 3 . 0 3 0 0 0 - 3 . 3 0 0 0 0 3 . 0 0 0 0 0 -1 .0-000 2 . 0 3 0 0 0 2 . 0 Ô 3 C - - 3 . 3 0 0 0 0 - 3 . 3 3 0 0 0 3 . 0 3 3 0 0 - 1 . 0 0 3 0 0 l . - O - O O 1 . 3 0 0 0 0 - 3 . - U 0 C 0 - 3 . 0 0 0 0 0 3 . 0 0 0 0 0 - 1 . 0 3 3 0 0 . 0 . G -3 .03000 - 3 . 0 0 0 0 0 1 3 0 0 3 0 3 . 0 3 3 0 " -1 .00000 1 .00000 " 0 . 3 -3 .00000 I —3.3-00 — 3 .O ^L O C — 1 . 0 - 3 0 0 2*0 Male of Good Physical Fitness, Sedentary Male. Time (seconds) *5 r .CC3 0 G / 4.G0G0j -3.00000 n -0.0 tc 1 5 .J0 0 C3 L Z - .G ^ 12 . 0 V, « C G ____ -5.00000 -0.: J- 4.00000 ^ V - : . G I 1 3 * V jCvC '-b.oOOOO -3 .0 5 .C0 0 C0 -2.0 i i • -'-’'-CO -3 .GOCOO — 6.00000 -0.0 2 . 3 J u C V -3 . 3 12 . C . 4 4 G -3.JC0G0 -f.OOOOO -0.0 1 .0 — 3 . 2 5 .3.200 -3.JCGCG —- . 0 -G.J 60 3 .G -0 .: . 3 -3 .32G0C .0 -0.0 •3.0 -3.0 -Z.OGuOü -0 .0 _ -0 .0 3 .3G0 C0 ““ — 2 . 2 - 3 ~ -3.0 -0.0 -0.0 5 .OOOOO • - -c . 3 ~ J • C -2 .00.-00 -u . 0 -0.0 5.00000 — 0.0 1.03000 -1.0JOOO -0 .0 -3.00000 4 .OOCCj -4 .3:00 2 — 0 .0 -4.0GGG0 -2.0O00C ____ -I.OCOCO n o 3.00000 -2.2:00" -3 •C.CCO -4.0CGOO -y.00000 -3 .00000 1 . jjGOO — 0 .0' 0 0 2 -4 . JGCOO -0.0 -3.00000 1 .OOOOO -3 .GOwGC -j.0:000 6 .03000 -4.O0LOO 4.00000 -3 .GOCCC 1.00000 -4.22:0. 6 .0CG30 -4.GOCOO 5.00000 -3.0C000 —2 .OO^Gu -j.0200C 7 -f.OCCOO I .00000 — 3.LCGOO -7.03300 .00300 - 3 .c:coc 4 . J . 2 t- J — 4 . 0 ÛG Oiy -U.O -J.OOOOO ISO -7 .GCOCO - 3.00000 1 .0 j300 -3.00rc0 —0 . 0 -3.OOOOO -1 .GOCOO - 3 .2.2 0 . -I .JCCOO_____ -j.o ^ ... — 3.vGOOO I . u 0 ^ 0 0 - 2 .0 .^co -J .0 — J . J -0.0 -3.00000" —J.V — 3 . 2 2 c 0 -J .0 -4 .00 000 -u.O -3.30000 -G .0 -3 .00000 —u . 2 -0 .0 -0.0 -3 .00000 — 3 . oc 0G2 — # -0.0 — 0 . V -4.oCOOO — J M il -7 . JüOOO .00000 >v -i .U'JUOU ~ / -j.o iO /O -5 .J00U 3 /I ^ / 7.00000 H . 2 2 2 C 2 ^ 7 .2:300 y l.OuGOO H --1 .00000 O -c ../ / -3 .3 0 GCC \0 ' 2 .03200 L . -0.0 ^ -1.00000 — 2 .oGOOO ^ -2.33003 — 1 . 2 2 2 c 0 .03000 -0.0 y .uoooo -4.00003 —4 .J u 30 3 -4 .CC0C3 -3 . jOOOO -I .00000 — 4.JOOCO ' 6.03000 — 2 . . C' c c 0 — 6 .CCCOC — 3 . J0000 -j.OOOOO -4.30000 60 7 .0C3 0 C -2 .0 3 0 0 : — •>. J 0 2 0 0 -3.00000 -3.00000 -4.00000 7.00000 — 2 .002G 2 -n .30:00 — 3 .uGGOC 1 .CCoOO -4.00000 6 .3 JÜ00 -2 .3^0 "" -L» .31 GOG -2.2CGCC -3.00000 " -V . J — 4 .30300 S .00003 . 2 C 2 G G -3 .OOuOO —0 • u -4.00000 -3 .0 -i.OOOOC -7 . C C 2 C 3 -3 .00000 —0 . 0 -4.00000 -3 .0 -2 .croc 2 -7 .32000 -3.0CC0C -0.0 -4.^GC00 120 — V.O -2.22:^" -6 . C 2 c 2 2 -3 . JCOOO -0.0 —4 .uCCCo -3 .0 — 2.C.2C. -3 . 0 2 2 C G —4 .Ou^OO -0.0 -4.30UÜ0 -2 .OCuCO -2 .3 .0 0 . -1 .00000 -S. OOOOO " — 4 .00000 -4.00 000 -2.00000 2 . 2 J 2 G . I.30000 -5.0CU00 -3 .00000 -4.00000 —2 . J u 3 3 u -2.2:0^' . ü -4.00000 -2 .OOjOO — 2 .OCuCO -0 .0 — 5.0L2C2 -3 .3:000 - O .vOuOU -3.3 IBO 1 .00000 3 .0 0 3 0 . -i .00000 -3.000ÛU — 2.00300 I .00000 1.00000 4 .2.2 - . -1 .22:30 -3 .GG00C - 2 .OoOOO -u . 0 1 .uuGOO 3 .j""0 . -1 . c '2 0 2 0 -3 . 0 0 0 0 0 -2 . 0 3 0 0 0 —0 .3 1 .0ÛC00 3 . 0 2 2 G c -I .0:200 -3 . 0 0 0 0 0 -2 .00000 —0 . J 1 .00000 2 . 2 2 2 c . -1 .00000 -3 . 0 0 0 0 0 -2 .00000 -0 .0 1.00000 1 . 2 c 2 0 2 -i .03^00 -3. 0 C G C 0 - 2.UÛG00 -0.0 1 .00000 1 .2000: Female of Good Physical Fitness. Sedentary Female. APPENDIX 6 DATA COLLECTION FORMS I ' 3 1 o S ! S 1 5 ! 1 . 1 I : ! i . o o o 3 3 ' to 1° IS 1 ! ' i s J J I I 12 j 1 I . 1 i ! 1 1 1 u ! APPENDIX 7 OUTPUT OF PREDICTIVE MODEL FOR VALIDATION This section presents the actual predicted output of the predictive model for the series used in the validation testing. The results are presented for each series of tasks. The computer output shows the subject category, resting heart rate, power output, elapse i time, mean heart rate, and per cent of resting heart rate. The observed heart rate values (in beats/minute) were typed in separately. The series num ber (1-6) and subject category are presented at the bottom of each series presentation. Male of good physical fitness is MG. Sedentary male is MS. Female of good physical fitness is FG. Sedentary female is FS. 199 2 0 0 AC H = SP(1MSE FURI MALE GOUD PHYSICAL FITNESS KHR IS 5U POkEi\ OUTPUT FLAPSEL TIMl MEAN H ear r RATEPtRCENT PERCENT OF RESTING HEART RATE UATTS) (SECONDS) (BEATS/MINUTE) observed 50 0 58 100 58 50 10 66 113 69 50 20 69 120 73 50 30 72 125 _ 7 6 ___ 50 40 74 ■ 128 76 50 50 75 130 76 50 60 75 130 76 flS 70 75 130 76 85 80 79 136 82 85 90 82 141 -85 ___ 85 ...... Too 84 145 85 85 liO 85 147 85 85 120 85 147 . .. 85 85 130 85 147 85 85 140 85 147 85 0 ___ 150 85 147 — 85____ ' 0 ...... " I6v 80 138 ... 64 0 170 74 128 58 0 180 70 120 58 0 190 66 114 58 0 ?00 63 109 58 0 210 61 104 — 58 --- 0 2 20 59 ' 102 58 0 230 58 100 58 0 ?40 58 100 . 58 ------Series' 1 - - M T AC KcSPHNSC MALE GÛÜO PHYSICAL FITNESS RhR IS 58 POWER OUT PUT ELAPSED TIME mean HPART RATE PERCENT OF RESTING HEART RATE (WATTS) (SE Co(OS) (BEATS/MINUTE) observed 30 0 58 100 58 30 10 63 108 64 30 20 67 115 70 60 30 68 118 __ 72 60 40 72 124 78 60 50 75 129 80 60 60 77 133 80 60 70 78 135 80 60 8P 78 135 80 60 90 78 135 . 80 60 100 78 135 80 6v no 78 135 80 60 )20 78 135 80 40 130 78 135 80 40 140 76 132 73 40 150 75 129 .. 70 40 160 74 12 7 70 40 ITj 73 126 70 4u 180 73 125 70 40 190 73 125 70 40 Poo 73 125 70 40 2 10 73 125 . 70 _ 40 220 73 125 70 4 0 230 73 125 70 40 240 73 125 70 Series 2-MG 201 I RPbPOf^SE FOR* - MALE GOOD PHYSICAL FITNESS KHR IS 56 POWER OUI PUT ELAPSED riME ' MEAN HEART RATE PERCENT (WATTS) (StCni'iDS) (BEATS/MINUTE) observed 105 0 58 100 58 105 10 69 119 76 105 20 78 135 a; 105 JO 85 14 7 8 105 40 90 155 105 50 91 156 8 105 60 91 156 8 105 70 ..... 91 156 8 105 80 91 156 8 105 90 91 156 .8 105 100 91 156 81 0 110 90 156 83 0 120 84 145 76 0 130 133 65 0 140 71 122 60 0 150 66 115 .58 0 160 64 110 58 0 170 105 58 0 180 59 102 58 0 190 - 58...... 100 58 0 200 58 100 58 0 210 58 100 _58 0 220 58 100 58 0 230 58 100 58 0 240 58 100 58 0 250 ------58...... 100 58 ---- . . _ ■ S s r t e s 3 “^ ************************CARD I AC RESPONSE FOR********»*#*******' MALE GOOD PHYSICAL FITNESS RHR IS 58 PGwFR uUIPUT ELAPSED TIME MEAN HFART .RATE PERCENT OF RESTING HEART RATE (WATIS) (SECONDS) (BtATS/NINUTE) observed 85 0 58 100 . 58 85 10 69 119 69 85 20 79 137 80 0 30 84 145 o ' 40 ' ' ' 79 136 ... 74 0 50 ..... 74 127. 64 0 60 70 120 60 . 0 70 66 114 58 0 80 63 109 58 0 90 ______60 ______104 0 100 59 102 58 0 110 58 100 58 0 120 58 100 58 0 130 58 100 58 ?0 140 58 100 58 20 150 62 106 20 160 65 112 68 20 I7u 66 114 68 20 IBO 67 116 68 20 190 67 116 68 20 200 67 116 68 2 0 210 67 116 20 220 116 68 20 230 ■ 67 116 68 20 240 67 116 68 .Series 4-MG _ « « 1 ^ X * ! ^ X y* 0 « f o > 3" « > ar: c c c o o o o OCCOOOOOOOOOOCCOJI'J^ —* m « OOCOOOOOOOOOOOOOOOOOOOOOO -H m — 7_ * -5 T) m * t/> w c * — c Cl * c * X« X c * c -4 « 1 * « f * * « rr * J N f\j fo rv ^ fc.* ^ — r- * f\) Pu M ^ ru *-» ►- r j**v^-o^cr-Nj >vn^ UJN'^O^CX'JO'VJ» T Lk, r\j V" > * 4' U.N >— O sC VI ^ oJfu*—o*ûCD-^>u^.r\*Jhoi— \j* > ooco ooccooc OOOOOCOOC O O O m X * ‘OOOOOOCCOOOOCOsOOOCOOOOOOOmX 0 ir * ,' I ! f i t / ' C -n 0 « 0 0 » Z c 0 n 1 2 0 3 > 0 0 i» cr -4 3 X CO 0 X r 0 ? 0 -D %X X ,11 % H' > I T > X -c 0 X -< 0 1/1 j CO 3 X X X cr 0 x> (r 0 x> X > r“ CO > r- CO r rn X m X 3 Jl 3 U-: 3 -»► m c Tl Z m CD *T\ Z CO 3 p* CO rti z -4 m U ui envn u en ^ en x 1 m Ui ) fu 00 ^ O: CGD^Crvf'PsOL^Wlk.W Lk,W^WWW^WLkf\jf"ODCD > Z (D V^WLw'WUJWU^WLwi CD a oc cc CD 03 OD CD Z 0 -1 % m X m •T) cr* m (/» c CO m 4 / 1 3 H* ~s > CO X H Ni > co X 3 75 * (D z X * 0 > -H « * CÛ CO Z # z * c * c « ro O s -n 7* * V —4X « 0 m > * m > * 1 * JL * to m * m * B * ♦ • • « X* m * X « 73 0 * o OOOOO^f- — f^>rsjfNjrvjr\jf\jrois;isjN>rvjNjfor*j!sjF-o m * ruN3rur\3N)N>rUN3N3N>rjN)i >00000000000 m o^N)^*<4'~^^«J)u z z c 0 I 1 m m > > ?3 ;d 73 ;o > > O o a* cr CDDDCOCDCOCT>-f^COLOU>U>COLOCUU)UJCiJCOCAJ^LnCn'*-JOCOrD 03^4:^4=^^^4^-P^4i»4ïk.^iifc4i»COCE>COCOCOCOCOCX)COCOCOCOrt> 203 AT RESPONSE FORo< MALE ScDEMTARY RHR IS 76 POhER UUrPUT FLAPSEn TIMt' MEAN HEAP T''RATE' PERCENT OF RESTING HEART RATE' (WATTS) (SECÜNLSI (BEATS/MINUTE) observed 0 no 76 100 76 no 10 68 115 85 no 20 94 123 30 _ _ 94 no 97 127 96 ____ 110 40 ' 98 129 100 no 50 99 130 60 100 no 99 130 100 70 99 !/•; 130 100 175 80 104 136 175 105 90__ 107 141 109 --. 175 ■ 100 no' 145 175 112 110 111 146 114 175 120 112 147 ^ 114 175 130 112 147 175 140 114 112 147 114 0 150 112 147 1 oO — 114 - ' 0 105 ■ 138 110 0 17v 99 131 102 95 0 IPO 125 95 0 89 :90 118 88 0 20C 86 113 85 0 ____ .210 82 _____ 108 --.82 0 220 81 .. 106 81 0 230 79 104 79 0 240 77 102 - 7 7 - ""§'ërires~r-lïS RESPONSE MALE SEPt-NTARY RhR IS 76 POWER OUTPUT ELAPSED TU,^ MEAN HEART RATE PERCENT OF RESTING HEART RATE (WATTS) (SECONDS) (BEATS/MINUTE) observed 75 0 76 100 76 75 10 87 114 75 20 89 118 90 135 30 92 121 93 - 95 135 40 .... 9 7 127 135 50 100 132 98 135 6P 103 135 102 135 7o 104 136 104 135 «0 104 136 104 135 90 104 136 104 135 100 104 136 104 135 110 104 136 104 135 120 104 136 104 90 104 130 103 136 104 90 140 102 134 90 104 150 100 131 103 90 n o 98 129 100 90 170 96 126 98 90 ll'O 95 125 90 98 190 95 125 98 90 20P 95 125 98 90 ^ 10 95 125 98 90 2 20 95 125 90 230 98 95 125 98 9 5 'K- 125 98 r M r TJ *oQJ > > L nt-HCOOCMCvJCMCMCSJi^O^COmcSJ S- (Uu30omo«-4t-HCMCNjCNjcsjcMcvjt-HOOOOCT>mocoinoa^oorN» O) VÛCOU>OCO PLwür) LUT Pur ELAPSED TIME MEAN HEART RATE PERCENT OF RESTING HEART RATE (WATTS) (SECONDS) lUEATS/MlNUTEl observed 0 0 76 100 76 0 10 76 ICO 76 0 ^0 76 ICO 76 0 30 76 ____ 100 76 . 0 40' 76 100 76 0 50 76 100 76 0 60 76 100 . 76 0 70 76 100 75 0 flO 76 100 76 0 90 76 100 _ 7 6 . 90 " 100 76 100 76 90 110 8/ 114 86 90 120 91 120 . 91 90 130 94 124 93 90 l4u 95 125 95 90 150 _ 95 125 __S7 90 16u 95' 125 97 90 1 7u 95 125 97 90 IRQ 95 125 97 90 190 95 125 97 90 200 95 125 97 90 210 9 5 125 _ 97 90 '220 "95 125 97 135 23u 95 125 97 135 240 99 130 _ 104 Series' 5-MS RESPONSE FOR*'***#*******#************ MALR SEDENTARY KER IS 76 POWFe UUT PUT FLAPScD TIME MEAN HEART RATEPERCENT OF RESTING HEART RATE (WATTS) ( Sl CDNDS) ( bLATS/.M INUTE) observed 14 J 0 76 100 76 145 10 91 119 89 93 20 97 128 95 9v 30 96 126 .... 96 90 4u 9 5 125 99 9J 50 95 125 99 90 6u 95 125 99 90 70 95 125 99 90 no 95 125 99 90 90 95 125 . _ 99 90 100 95 .. . 125 99 9^ 110 95 125 99 90 120 95 125 . 99 90 130 95 125 99 90 140 95 125 99 9v 1 50 95 125 99 0 I'u 95 125 99 0 1 7b 90 119 99 0 100 84 111 . 99 0 1 90 81 106 92 0 200 79 104 88 0 2 1C 78 103 _ 76 0 2 20 ..... 7 7 ... . 102 76 0 230 77 101 r .■’4" 76 7 7 101 76 206 AC KESPnfJSE fDR# FEMAI, E GOOD PHYSICAL FITNESS RHR IS 72 POWEK OUTPUT ELAPSEL TIME MEAN h e a r t .r a t e PERCENT OF RESTING HEART RATE (WATTS) (SECONDS) (BEATS/MINUTE) 4A observed 0 72 LOG 72 45 ■ 10 82 113 78 45 20 88 122 88 45 30 126 45 '...... 9 2 ___ ” '40 ------126 . 94 j 4 50 91 126 94 45 40 91 126 94 8u 70 91 126 94 80 80 98 136 100 B u ___ 90 _ 103 143 — 103 PO 100 ■ 103 143 . 105 80 no 103 143 107 80 120 103 143 , 107 80 130 103 143 107 80 140 103 143 107 0 l50 _ 103 ______143 107 0 1 6o ■■ 98 136 100 Ü 17v 84 116 88 0 1«0 79 109 ^ 82 0 190 76 105 77 0 200 74 103 74 0 210 72 100 __73 0 220 72 ' 100 72 0 230 72 100 72 0 240 72 100 ..__72 Serie's 1-P3— , 4 , RESPUNSE EUR*******»»#*»****»#**«#*** FEMALE GOOH PHYSICAL FITNESS KHk IS 72 PC..EK OUTPUT ELAp ->Eu TIME MEAN HEART RATE PcRCEN OF RESTING HEART RATE (WAI1S ) (SECUNIS) (BEATS/MINUTE) 25 observed 0 72 100 72 25 10 78 108 80 25 20 83 115 82 55 30 84 116 55 _ -84 40 90 126 90 55 50 94 130 97 55 6u 94 131 97 55 70 94 131 55 97 «0 94 131 97 55 90 94 131 97 55 100 94 131 55 94 97 1 10 131 97 5 5 120 94 131 97 35 130 94 131 35 97 14 0 92 127 95 35 150 89 123 35 87 94 140 12 L 92 35 I 17u 8 121 91 35 1"0 8 7 121 90 35 190 07 121 35 07 90 2QP 121 90 35 210 0 Î 121 . 90 35 220 87 121 90 35 230 8 I 121 35 24P 87 90 121 90 Series 2-FG 207 . AC RESPONSE Ff)R< FEMftIE GOOD PHYSICAL FITNESS RhR IS 72 PCHEF UOTPUT ELAPSED TIYb MEANHEART RATE PERCENT OF RESTING HEART RATE (WATTS I (ScCJNDS) (REATS/MINUTE » observed loo 0 72 100 100 10 85 LIB 100 20 9 3 129 1 0 0 ___ 30 _ 99 137 100 ' " 40.... 104 145 100 5v 108 ISO 100 AO U P 153 100 70 110 153 100 60 110 153 100 90 110 153 100 100 ' 110 153 0 110 no 153 0 120 104 144 0 130 91 127 0 140 88 123 _ 0 ___ 150 83 115 0 ■ 160 ■ 78 108 0 170 73 101 0 1°0 72 100 0 190 72 100 0 200 72 100 0 210 72 100 0 22P ■ 72 100 0 2 30 72 100 0 240 72 100 O' 250 72 100 Series 3-FG AC RESPONSE FOR*: ************ F Eh AL E GOOD PHYSICAL FITNESS KH.R IS 72 OF RESTING HEART RATE (WATIS) (StCnNOS) (BEATS/MINUTE) observed 6u 0 72 100 72 66 10 85 117 85 80 20 92 127 93 0 34 97 135 98 0 40 '93...... 129 85 0 50 81 113 82 0 60 75 105 78 0 70 73 102 76 Ü 80 73 101 72 0 90 72 100 72 u 100 72 100 0 72 1 IP 72 100 72 Ü 120 72 100 72 0 130 72 100 72 15 l',0 72 100 72 n 140 76 106 80 1 5 1 6u 79 110 1 5 82 1 70 80 112 82 15 1 ur 80 112 82 14 190 80 112 1 5 82 200 80 112 82 1 5 2 K 80 112 15 82 220 80 112 82 14 239 80 112 1 5 :'4(i 82 UP 112 82 208 CARD! AC RcbPu.NSE FUR< t F'-'ALE GOOn HnYSICAL FITNESS RHR IS 72 PCKÈK UUTPUT El APScT ri"E MEAN HEART RATE PERCENT OF RESTING HEART RATE (WATISI t SuCUNOSJ I BEATS/MINUTE) observed 0 0 72 100 72 0 10 72 100 72 0 20 72 100 72 0 30 72 100 _72._____ 0 ■ 40' /2 100 72 Û Su 72 100 72 0 60 72 100 72 0 70 100 72 0 mu 72 100 72 Ü RO 72 100 -72 _ ' 100 '72 100 72 J3 110 80 111 83 3t) 120 86 119 87 33 130 87 121 90 33 14Ü 87 121 90 35 150 87 121 33 _90 ______16v 87 121 90 33 170 87 121 90 35 180 87 121 90 35 190 87 121 33 90 200 87 121 90 35 2 10 87 121 _90 ______35...... 220 8 7 121 230 90 55 87 121 90 55 240 91 127 95 Series 5-FG : vvwwwv vw w v o e C A R U I AC R l SPUNSE f e m a l e GOCU) PHYSICAL FITNESS KHR IS 72 PCwn< UUIPUT FLAdSFL III' MEAN HEAR I RATE PERCENT OF RESTING HEART RATE (WATTS) (SECriN PS) (8EATS/MINUTE) observed 60 0 72 100 72 60 10 84 117 84 35 20 91 127 91 35 30 89 123 _ 91 35 4U 8 7 121 91 35 50 8 7 121 91 35 6o 87 121 91 35 TO 87 121 91 35 8" 87 121 91 35 90 87 121 . 91 33 100 8 7 121 91 33 110 87 121 91 35 120 87 121 91 35 130 B7 121 91 35 1 4 0 87 121 91 35 150 87 121 91 0 1 60 8 7 121 ' ■ 91 0 1 lu 85 119 87 0 1 80 80 111 80 0 190 75 104 74 0 200 72 100 72 0 2 10 72 100 72 0 220 72 100 . 72 0 2 Ui 72 100 72 Ü 240 72 100 72 Series 6-FG 209 CAPQ I AC RESPONSE FOR% e f w ai E SEDENTARY RHR IS RC HLWEK UUTPUT FLrtPSFO TIME' MEAN HEART RATE PERCENT OF RESTING HEART RATE...... (WATIS) ISECONOS) I REATS/MINUTE) observed 6Ü 0 flO 100 80 6U 10 91 114 ...... 86 60 20 96 121 91 60 _ jO 100 125 95 6U 40 102 ' 12 7 ..... ■ ■ 100 60 SO 103 128 103 60 60 103 129 103 100 70 103 129 - 103 lüO PO 111 139 103 100 90 115 144 _ 110 LOO ' IOC 146 ■ " 112 ' 100 110 117 146 113 100 120 117 146 114 100 130 117 146 114 100 140 117 146 116 0 150 117 146 116 o' . 1 6u 114... . 142 .. . ' "'lio'"' 0 170 lOfl 135 115 0 1Ü0 103 128 110 0 1 VO 97 122 98 0 200 91 114 90 0 210 07 109 87 0 2 20 64 " 1 0 5 ■ ■■ ■ -...... - - ■ '84'" ' 0 230 62 103 32 0 240 80 100 80 Series 1-FS RESPONSE F0R*»**4»******************* FEMALE SEDENTARY RHR IS 60 PChF^ UUTPUl ELAPSED TIiM l MEAN HEART RATE PERCENT OF RESTING HEART RATE (RAT 1S ) (SECONDS) IHEATS7MINUTG) observed 40 0 80 100 80 40 10 65 106 90 40 20 90 112 93 75 30 92 115 94 75 ■ 4L 101 97 75 50 105 131 99 75 60 107 134 100 75 70 108 135 101 75 GO 106 135 102 75 90 108 135 103 75 100 108 135...... 108 7 5 110 108 135 108 7 5 120 106 135 108 50 130 108 135 108 50 140 106 132 108 50 150 103 129 105 50 U V 101 126 103 50 1 7o ICO 125 101 50 1"0 lOo 125 100 50 103 100 125 99 50 200 100 125 99 50 c 1C 100 125 99 50 220 100 125 99 50 /ir' 100 125 99 50 24 0 I 00 125 99 Series 2-FS 210 RlSPuNSE fn^************************* FcMAI.E SEDENTARY Î KHR IS me ^ hCWER UUTHUT "■ E L A P S c D T I M E ' MEAN HEAR I RATE PERCENT UF RESTING HEART RATE” " ^ (WATfS) (SuCUNDS) (BEATS/MINUTE) observed 12 b 0 80 100 80 12b 10 95 119 ” 88 1 12 5 20 106 133 94 9 125 30 113 141 100 : 125 40 118 148 105 125 50 , 123 154 111 125 60 125 156 120 12 5 70 ■ ■ 125 - . 157 - - 125 ' 120 Pu 125 157 125 125 90 125 157 125 12b 100 ------129 ■ 157 - ■■ ■ 125 0 110 126 157 125 0 120 120 150 120 0 130 111 139 114 1 0 140 105 131 108 - 0 150 98 123 92 0 ... " " '16U ” ' '91 114 ■' " 85 0 170 87 109 80 0 180 84 105 80 0 190 82 102 ' 80 ... 0 200 80 100 • 80 0 210 80 100 80 0 220 80 100 ■' 80 0 230 80 100 80 0 240 80 100 80 Series 3-FS RESPUNSE F OR <'*******$**************** FEMALE _ _ _ SEDENTARY ...... KHK IS 60 PCbEK UUIPUT CLAPSEO TIMF MEAN HEART RATE PERCENT UF RESTING HEART RATE 100 0 80 100 80 100 10 92 115 90 luo 20 99 124 95 0 30 105 131 103 0 40 101 127 103 0 50 97 122 101 0 60 93 11,7 99 0 70 90 112 98 0 80 87 108 95 0 90 84 105 92 0 100 82 103 ■ 90 0 110 81 102 88 0 120 80 100 87 0 130 80 100 86 30 140 80 100 83 30 IPo 84 105 85 30 1 60 88 110 87 30 I /o 90 112 90 30 IRC 91 1 14 94 30 n o 93 116 94 30 200 93 116 94 30 210 93 116 94 30 220 93 116 94 30 2 1C 93 116 94 30 240 93 116 94 Series 4-PS 211 RiiSPriNSE FOR* hfcMAI C ScDeNT\RY RhK I^ 80 .... PCwEK bUTPUT ul APiTP TIME ilEAN HEART RATE PERCENT OF RESTING HEART RATE 1 WATTS) { Sl CJ.'JPS) (BEATS/MINUTE) observed 0 0 80 100 80 0 10 80 100 80 0 ?0 80 100 80 0 30 80 100 80 0 ...... " 40 ' 80 100 80 0 50 80 100 80 0 60 60 100 80 0 70 60 100 80 0 Po 80 100 80 0 90 80 100 80 so 100 80 100 80 50 no 88 110 92 50 120 93 116 95 50 130 96 120 98 50 l40 98 122 101 50 1)0 99 124 103 iO .... I tt\j 100 125 103 50 no 100 125 103 50 160 100 125 103 50 190 100 125 103 50 200 100 125 103 50 2 10 100 125 103 50 ...... 220 100 125 ' .... ■ 103 75 210 100 125 103 75 240 105 131 112 Series 5-PS RESPuMSE FI3R»** *********** *********** F EMALE SEOLNTARY khk IS 80 HC.WFis UUT PUr FLAPSEO riKE MEAN HEART RATE PERCENT OF RESTING HEART RATE (WATTS ) (Sf CÛNiDS ) (bEATS/MlNUTE) observed Bu 0 80 100 80 80 10 95 119 88 50 20 10) 129 96 50 10 101 126 102 SO 40 1 0 0 ...... 125 102 50 50 100 125 102 50 60 100 125 102 50 70 100 125 102 50 80 100 125 102 50 90 100 125 102 50 100 100 125 102 50 110 100 125 102 50 120 100 125 102 50 130 100 125 102 50 140 100 125 102 50 150 100 125 102 0 160 100 ■ ' 125 102 0 1 fv 95 119 100 0 1 PO 91 114 88 0 190 88 110 84 0 200 85 107 82 0 21o 83 104 80 0 220 82 102 80 U 2 )0 81 101 80 Ü 240 81 101 80 APPENDIX 8 DOCUMENTATION OF PROGRAM FOR THE PREDICTIVE MODEL Input Card Specifications cc. 1- 2— subject category, MG, MS, EG, FS or XX (for last card) cc. 4- 5— resting heart rate (beats/min) cc. 7 — number of tasks (2 or 3) cc. 9-11— initial value (%RHR) cc. 1 3 -I5 — 1st task work load (watts) cc. 1 7 - 1 9 — 1st task duration (seconds) cc. 2 1 - 2 3 — 2 nd task work load cc. 2 5 -2 7 — 2nd task duration cc. 2 9 - 3 1 — 3rd task work load cc. 33-35— 3rd task duration Any number of input cards can be included with XX as end- of— file • List of VarVariablesiabl es (in order of appearance within program) El, E2, E3, E4 4x19 arrays which contain all hard FI, F2, F3, F4 data heart rate patterns— row 1, is MG, Gl, G2, G3, G 4 2 is MS, 3 is FG, and 4 is FS. HI, H2, H3, h 4 Al, A2 , A3, A4 Appropriate hard data arrays are Bl, B2, B3, b 4 selected and transferred to these 19 Cl, 02, C3, C4 element list for computation. (See Dl, D2, D3, d 4 Chapter IV for definitions) WA, DU 3 element lists for work load and dur ation Z 1 9 element HR pattern not adjusted for time (%RHR) ZT 18 element HR pattern adjusted for time (%RHR) ZM 18 element HR pattern (heart rate) 212 213 L,H 19 element low and high patterns SC, SUB, PF Character for subject category, sex, and physical fitness IV Initial value IRHR Resting heart rate I Number of tasks sss Expected SS %RHR IC Test constant for L & H selection R3 Ratio (see Chapter IV) R1 Ratio (see Chapter IV) R2 Ratio (see Chapter IV) IC4 Test constant for SC IT Time IWA, IZM, IZT Integer for ¥A, ZM, ZT XO, YO Dummy lists of 19 elements 21k start 1-15 Read Hard 16-52 Data Read Input Card St op Load Correct Hard Data The following loop is Patterns completed for each task in input card 103 Task ^10 100 = SSS Watt a 87-102 Comput e SSS 4- .105-197 See Figure 12 Load C___ Chapter IV for L&H Detailed Flow chart Flowchart of Program for Predictive Model. Comput e ecovery ZT 204-209 Compute 210-216 Det ermine Shift Magnitude Jy 217-291 Compute ZT Compute ZM /^Ist Print Task Headers 287-301 Print ZM&ZT Xast Task 216 PROGRAM FOR PREDICTIVE MODEL (WATFIV) c Tl IS R K U b R A M C-U'J t\G US CD ni RRLOICr AN INDIVIDUAL'S CARDIAC c Rr:,K:-'iur- n, a s e r i e s di f IXI n iwrcNSTY iasks c ARR/^YS CfljUf A.-jU h Are rtic ARRAYS WHICH HOLD HARD DATA IN RHR c PDW 1 IS "ALF-OUUD c Ki.W , IS MAL E-S -L'ENrARY u KliV. 3 IS ELMALr-uuijn c ki;l. 4 1 c f l-nALE-SFnENTARY DI.'U NS lu" L L( 4, 10) , ':214, 19) , E3I 4, 19» ,E4( 4, 19) r. I ■ ■ IS I UN F 1 I 4 , 19) ,t c' ( 4 , 1 9 I , f 3 ( 4 , I 9 ) , (- 4 ( 4 , 1 9 ) 3 ;i !.•: !US I UN G 1(4, 1 V) ,u 2 (4, )9), u3( 4 ,19),04(4,19) u DIM MS ION H U 4, 1 / ) ,l'2(4, I9),li3(4, 19 ) , H 4 ( 4 , 1 9 ) m RRA v S A , d ,C ANH n ARE ARRAYS WHICH HCILD THE APPROPRIATE L'.D-LL FA TA FPR Cu)-.RU F A T luN Al, m ’’, A3 a n d A4 AKF 100 fU 100, 120, 140, AND 160 RESPECTIVELY 5 la ME N S I UN A M 19) ,A2l 19) , A3( 19) , A4 IL 9 ) bl, F2. P3, ANu 84 Ak E 120 TP ICO, 120, 140, AND 160 RESPECTIVELY 6 Dl Ml IS I UN L 1 ( 19) , P M M ) ,E3( 19) ,U4( 19) '*1, ^2, 03, ANC C4 ARE 140 TO 100, 120, 140, AND 160 RESPECTIVELY 7 UinENSIPN C l ( 19) ,C?( 19),C3( I 9) ,C4( 19) II, C'2, C3, ANT - U4 AkE 160 - I'P 100, 120, 140, AND 160 RESPECTIVELY Ü OM'FNSI'^N M'K 19) ,L2( i 9 ) , r j ( 19),r-4( 19) AkKAYS wA AML DU ACCEPT wATTS AND DURATION UP TASKS 9 riFn'lSiUN ,.A( 3) ,PU( 3) " "7 ' ...... ARRAYS 7 -FK Pa TTHN IN RHR ZT -ADJUSTED FOR TIME ZM -ZT MEAN HR 10 CIM-NSIPN Z U 9) ,ZM1 lb ),Z ri 18) ARRAYS L AND Li ARE h^RK AREAS THAT HOLD THE LOW AND HIGHHARD DATA FOR each PREPICTEU HR PATTERN 11 KÉAL I ______Ic u II- No ION L ( 1 9 ) , hi 19) " ' ...... 13 CHAKACTE" sr«p,c(ja<>6,PF*2l RE AC IN HARP DATA...... 14 J= 1 15 5 IF (.1 .F0.5) GO TU 95 lb 10 rURKAT (19F4.0) 17 KEAC(5, 10)1 ALIK),K=l‘, 19)-'^ - - -...... -...... in RF«n(5, LG)lA21K ),K = i, 191 ’ 9 RnAL'l 5, ’ C) ( A3( K ) ,K^l , 19) ^0 REAP(5 , iO) ( A4lK) ,K = L ,19) 2 1 REAM 3 , 10) ( Pll K ) ,K = 1 , 19) 22 KÉAM 5, 10) I F3:l K ) ,K = l , 1 9 )______23 RFA^l 3, ID (1'3( K ) ,K = 1 , 19) ' ■ " ...... ' ■...... 24 n'^AM 5 , 10) ( R4l K ) ,K = L , 19) ^5 Rf AM 5, LOI I Cll K ) ,K = 1, 19) \ ] 20 REAM 3, 10) t r.2( K 1 ,K =1, 19) 27 read 19,1u ) ( C3l K ) ,K =1,19) 2R READ 5, 1 0 I ( C4( K ) ,K^l, 19)____ 29 ' RLADl 5, 10) I rai K) ,K^1 , 19)' 30 RFAF ( 5, 1C) ( [121 K ),K = 1, 19) 31 RPADI5,10)1P3lK),K=1,19) 32 READ!5,101(041K),K=1,19) LPAU DATA TP APPPQPRIATE HARD DATA ARRAYS 33 CP 5u Y = 1,1 9 ______■_____ 34 E l(J,K )=A1( K ) 35 E2(J ,K ) = A2(K ) 36 E3(J,K)=A31K) 37 E4 ( J ,K ) = A4( K) ...... - ...... 38 I 1 ' J , K ) = P1 I K ) 39 F2(J,K)=B2(K)______40 F3(J,K)=E3(K) 217 4 1 F 4 ( J , K ) P4 ( K ) 4T u 1 ( J , K ) = r. H K ) 4 3 021 J ,K t --C2(K ) 4 4 G3(J,K)=C3(K ) 41 o4 (J , K »- C 4 ( K ) ‘I t Ml (J , N )= r i ( K ) " ' ...... 4 7 M,’( j,K ) = r:2iK) 4P h3(.l,'" ) = C3 ( M 40 h4( J,K ) = D4(K. ) 1)0 50 CU:H I 1 Nu F 5 1 J= J <■ J. 4/ ÜM r f" 4 • - ...... • ■ 1,'iP'ir nATA ^C))SohJuCr CAFcGü'lY, IRim-RESTINO HEART RATE, I = NUM tajk5, iv=iMiriAi value, wA^wArrs, du=durat[on. R E A L A E.a TA C a RO rOR UNE INDIVIDUAL 53 0 s R l A l ( 4 , I C O ) s c , 1 KM<, 1, IVfWAl I »,DU(I),W A (2),DU(2),WAI 3),D U (3) 54 10Ü Iu RF a T (A2,13,12,14,644.0) XX lU THE SC riFl.n I,'inir,ATES LAST CARD TERMINATE PROGRAM .... 55 IF (SC.EC. •ax*) STOP f O l T c Ki'l I "i E APP ki^PR I AT E H A R D PAT/\ a r r a y cFXTCwS1 ON» A CMA a ACTER V A R I A H L F IS U S c D WITH A RELATIONAL OPERATOR 56 TF (S'-.EC. ' K.r,* ) uU Tu 1 Jl <' t X I F ■ J 5 1 nw* M L F*Ai\.» CI E R V A R I A b L E IS U S E D WITH A RELATIONAL OPERATOR 4 7 IF (SC.ct. ••■S') Gu TO 102 <-FXT£,<5 IGN* A u) A'\ACTFR V A 3 Im CLF IS USED WITH A RELATIONAL OPERATOR 5o IF ( S C . 4 ^ . '40') uO TU 103 t X T £ i'i j ITN* A C H A R A C T F R VARI al'Ll IS USED WITH A RELATIONAL OPERATOR 59 IF (SC.EC. '4S • ) on TO 104 < L-XTE.JS Iu,\» A CuArNACTEK VAT I ALLE IS USED WITH A RELATIONAL OPERATOR oij lul J= 1 ■ .... . 61 GC TO 106 6? 102 J^2 63 GU TO 106 64 103 J= 3 65 GO TO 106 66 104 J = 4 C LH a O .\PPRnPKIATt HARD DATA INTU COMPUTATIONAL ARRAYS 6 / 106 CO 107 K=l,19 66 Al(K)=F1(J,K) 69 A? (K ) = F,il J ,< ) /u A3(K)=E3(J,<) 7 I A4(K ) = t4(JJ 7? 6’ (M=F1( J,K) 73 R2(K) = F?(J,i<) 74 E3(r.) = F3 (J , < ) 75 b4(K)=F4(J,K) 76 Cl (K)=GU J,R) _ 77 C 2 ( K ) = G2 ( J , K ) 76 C 3 ( R )= G3(J ,X ) 79 C4 (K )=G4( J,K,) 80 01 (4)=H1U,K) 81 02(K )=H21J,X) 02 0 3 (K)=H3(J ,< ) U3 04 ( M = F4( J ,K ) 84 107 CONI INUF THE FCLlOWING L O O P IS c o m p l e t e d o n c e FOR EACH TASK- 2 OR 3 85 on 940 Mai, 1 IF T A SK R E c IIIr ES L E S S t h a n 10 W A T T S SET S S S = 0 8 0 IF ( r. A ( M J - 1 0 ) 150,lu9,199 C H E C K SDBJ l CI LA I EGOR Y MaMALE.F = FEMALE,G=GOOD P F ,S = SEDENTARY 218 "7 lu9 IF (bC.tl. , •'•■iG'j GO Til no rxTFU'., IC'N* A C HA.', AC r h '< VA< 1 AIM. F IS UScC MITH A RELATIONAL OPERATOR IF (SC.FL , 'H F ' ) uO Til ■L A (t JF. 1 UNX: ^ cHA^ACTU: Vh'î I A I) I. E IS oSCO WITH A RELATIONAL OPERATOR h y IH ( bt . L U G FI TO I JÛ ■ I. X r Liv,,I IvN * A uF'A \ AC I K VAX I Al l L I S USED WITH A RELATIONAL OPERATOR 9j IF IbC.'-C .'I'-*) uU TU l-tO C Ci'l-.Pul I FXPFCTLu SFl ADY STATE RUR (SSS) c HPR wf, XT'. NS 1 UN" A CHA AC TFR VAXI..HLE IS UScO WITH A RELATIONAL OPERATOR 9 1 I 10 j S ) = . '• A( M) + IGo . J3 92 1CA = I 9 3 ur TP ifo C FuR MS 94 120 SSS = .?:)9*WA(M| + 101.443 9j 1CA=2 94 GF TP 16v _ C FUR FG ...... 97 130 SSS = .4nA>'.= rtA( M) + 104.3G6 V8 ICA=3 99 CP TP lAC C FOR FS luG 14v SSS=.AJ1*WA(K)+Iü2.>49 _ 101 IC4=4 102 GFl TP 140 103 15u SSS=100 104 160 CDNTINuF 103 IC=0 L I H I \ S bGi'-iEl» 0 L I >- rt N I l'y ê ,b WHICH HAHÛ UA TA ARRAYS TU USt-HÎGH ANU LOW 106 IF ( I '/ - 12 0 I 170,170,175 IJ/ 17J iC=IF,+ I lOR G" TP 200 lu9 175 1 F (IV-l'iO) IbO, laO,185 1 10 18P IF=IC+2 111 GO IU 200 1 12 183 IF (lV-140) 190, 190, 195' 1 13 190 IC=IC+'3 114 Gu TO 200 1 15 195 PRINTIV IS GREATER THAN 160 RHR* 116 GP in 95 1 17 200 IF (SSi-120) 210,210,215 1 1 8 2 10 lC=IF. + ij 119 uu TÜ 250 120 2 15 IF ISSS-14CI 220,220,225 12 1 2 20 I C = l C + 2 0 12? GL TO 250 123 2 ^ 5 1 F ISSS- 160) 230,230,235______124 230 i F = I C + 3 u 12 5 GF TP 250 1 26 23 5 PPINI,'SSS IS GREATER T H A N 160 R H R * 12 7 GP TO 95 12 8 250 TF (IC-ll) 270,265,270 129 265 IF (IV-SSS) 26/,267,266______130 266 CALL CJPY (L,Li,19) 131 C A L L r.Pl'Y Ili,u2, 19) 132 GO 10 A JO 133 267 c a l l CMPY(L,Al,191 134 wALL Cf.PY(H,A2, 19) 135 GP I 0 4UU 136 270 IF I IC-I2)2R0; 272,280" 219 Il 7 2 7? II ( A (f 1-0. 0) 2 7 5, 2 73, 275 1 i ? 7 j r.Al C'iRYlL, 1’ 1, 19) 1 ) 1 r,\i. Cul’V (11,61,19) 1 ‘i 7 u - C ) 5 L lA 1 ? 7 5 r M i. C, "Y 1 L, t 1,19) 1 M,’ CAl Cl HY (II, C2, 19) l'i j GP (I G G i ‘f 't c 5 0 . f 1 C - 1 J ) . y ), 2 'j 1 , 290 1 •. A a P 1 TC ( C.l C.'I'C ' 1 I.C T.. 20 2 ' r X I i.rr.,11 ■ iX ■■ ft Ll i/i t c r vA.iia.iLF ic ii'juc c ITII A RFLAIIGNAL (IRtRATHR I A f K ( c .1 c. ' ( c ■ ) 11, 252 "t XI L.'JS1 l.'N'X A Cl'A ACILil VAiXlAbl.L' 15 US a G WITH A RtLATlONAL (APERATGR 1 A / üvv Ü 285 1 4 U Abc 11' .lA(^.)-6.ul 213, 214 ,263 lA y A Al V. R I [ ( 7, , 3 1 9 1 G( C y 5 i'xl 2ÜS CAL C.iRY( L, Cl, 19 1 1)2 CAL C..9*Y(H, Cl, 19) i )) GC n y50 l'^A a 35 ir ( A(, J-O.v) 267,204,287 D ) 287 CAL C RY(1,C1,19) 1 3C. Cm L c ,. 1* V (1- , r* ? , 1 ‘9 ) 157 GC 0 Ce 1 5 0 A 7u IL lC-21) j ÜG,29F,500 l5 CAi.l C II'V ( L, n ), 10) 1 n oALL Cm I'V ( h, U4, 1 j ) 1 •): Ol' 1 0 .,0^ 1 ) ) J4t, Kin ( I., j 10 ) 1 'j‘, Ol, n 0 5 1 34 / OAl L C‘"’i'Y (L , C 3 , L 0 1 L'JI- C M L C ,t’Y I h, 0-,, i'>) in ! or Tl’ ',00 C KniT i,n' fu n, i‘o< ■ PM / r f u < rpcovcky p a t t o k .ts r. tir IV oKEAl FR T ' \'j 120 I )'■ ' J Dv K3^ ( I V-i ( -) ) / i I' ( _ »-Ll 2 ) ) ir) ZT( I) = 1V CL 340 ue=’,12 .01 Zr(KiM = lim'^*l)-l(Kri + ll)«R3*-LlKb+ll ti u ^ jf.n OCNT I'l Jfc .0 i or TO JlD 4^0 1 r L oib-L ( 1 r ) ) •* 1 .,405,410 / )‘J 405 L^oo Cl.RY (2,0,191 2 Of O'" Tf ‘,2 1 c Ki n roh patil |‘c t .'JE=,'1 sss a Nr the low ss and the hard D A T A H- L 207 410 Kl = (SSS-L( 10) )/2u.O c CL. n'uTi: T H L FXRcClLD HR PA TTER'N AND STURE IT IN Z cr 4^-1 K = L , 1 -) ?. 0 420 Z( K ) = I t h( K )-L( K ) IKR UK K J 1 c AI'JI'ST IWDLX Fur TIME IN 10 SECOND INCREMENTS ; I'j 42i nilV-SSS) 435,435,423 .11 423 cr R = c. I ) ^ \ 2 43 4 7 u ( 1 V-Z ( .1 ) I / t Z (.1* l)-f ( J ) I 24 4 4 8\v / I ( 1 ) = I V C ' Ir niL FYPuCrcn nK PAriEHN adjusted for time and store in zt 24 G [Hj ‘I'Ju K = ? , 1 d 2 40 ZI(K)=:((Z(j*c)-/(J*l))«RZJ»-Z(J*l) 24 t Ir t z u -*i).t:'%zn » )un in 500 J = J u 2-, 9 4 60 mwriNur prn 3 Û6 i^L' Siu K P = K , IR 231 ■J 10 Zr(KRi^sss C v' "t'i,TP IP kattfrn in mean hr for a given resting hr 2 32 3 ! 3 rn f)?j K = i,io ■ ■ 2 33 3 20 Z" ( K ) = ( ( Zf ( K ) *IM1R) / 100) 2 34 IF 1 '■ .‘IE. I ) GO yn 61S C D-TTi-^'INl FEAL'ING Va k IADLES '...... 233 "t., 10 ( J , A? , yAA SA6) f ir.A 2-Jd 3 4v I’ALc ' 237 Ef-'bOnu Pl.YGlCAL FITNESS*' ~ :...... 2 3b on rr g60 239 S f 2 Ai'0 = ' m a l e ' 260 PF=' Sl DENTARY • - - - - 261 on rr r60 C.ÙC 544 '■Uu- ' FF,MALE ' L 63 PF = ' uJÛU PHYSICAL ' FI INESS* ...... 2 64 oL rc 560 2o3 3 46 '"L • r ûNiALE ' 2 6 6 pr = * r "DENTARY ' C PPIuT riEAniNG INFORMAT ION 26 / 36U W K 1 I L I. tj f 5 7u I 26 b 3 / 0 1 r:.',.-AT( LHl , ■ I", • C\^i:i AC“ RESPONSE' FOR2 5 I • ♦ ' ) ) ... 2 69 WKIT LIb,büGI SUE 270 5Ed FuPf-ATIiX.jll • ' ) , A7 ) ...... 271 wRiIE(6,590) PF 2Tc 89 0 Frnr’M ( IX , ?A ( • «),A?1) c7i Wk i r E ( o f 6uL ) I K HR ; 74 üOO FLP,*^Ar I IV, agi • • ) , 'RHR IS «, 13) ' 273 WRI1L Fh,dir ) y- dir rorpAT( IX,• • ) c PRI.a COLUMN FEm CINGS 27 7 WR I y: Id, d2C ) 2 7F d 2w r-rRVArilX,' PO/.LR OUTPUT ' , "ELAPSED TIME ' , 'MEAN HEART R IRATE ' , ' PdRCE'NT OF RcSTING HEART RATE') 279 NR IT F ( 6, Zi3d ) 2PC 6 3G Fl RFATI 3X,•I WATTS) '(SECONDS) BEATS/MINUTE D M ■ 2b 1 1T=0 202 6 9 5 K- 1 r ROUNn ALL HR AND Rhk OFF TÜ NEAREST' INTEGER ..... 20 3 00 d9P lX=i,18 2 A4 ZM( IX)=ZMI IX )+.S 283 ZT(IX)=ZT(IX1+.5 . - 2 8 6 69d vONIINUE c PRINT POWER OUTPUT, TIME, RHR, AND MEAN HR 2b 7 700 1 rt A - W A I M ) 20b IZF. = /M(K) ...... 209 I/T=/TIK) ...... 29 0 wRlTFU,,705) IWA.IT, 1ZM,IZT ' .. ... 261 7 0 S I r->kAf ( IX, Id, ItX, I 3, lAX, 15, 15X, 15) 2 9 2 IT=IT+10 293 i\ * K + 1 ■ 2 2 2 P / M /3Ü IP ( 1 T .LT . (r'ii( 1 ) n^0( ?) ♦out 3 n » Gf) TO 7 0 0 P S; T IN iT lA l VMbl; FOR N^Xf TA S K I v 0 o o ., ;v = Z f ( K ) 3 v 1 OOP cr IN'I F )0P Gu TU OS Û 0 J Ù N P 10/ SI uR( u r 1 NF Pfil'Y 1 xn, YO, N'U C Si'nKi’UTriÉ UPPY LÜALS ARRAY XU INTO YO BOTH OF DIMENSION NO 3UU OlS'Fir lUN ' IN P U T WORK LOAD IN WATTS, DURATION IN SECONDS, AND RHR ? 2 2 0 , 1 2 0 , 7 6 0 0 0 1 0 P R IN T ' INPUT WORK LOAD IN W A TTS , D U R A TIO N IN SECONDS, AND RHR' TIME HEART RATE 00020 INPUT W,D,R 0 76 00030 B = .t)»W 10 1 1 1 . 2 4 9 7 OOOUO A 1 = P * . 25 20 1 2 2 . 5 7 4 5 nnOLO A2=C-A1 30 1 3 1 . 1 9 2 3 ocoeo PRINT 'TIME HEART RATE' 40 1 3 8 . 0 1 1 4 0 C C 7 0 FOR T=OTODSTEP 10 50 1 4 5 . 4 1 3 1 60 OCOFO Y=A1*(1-(1/AE**(.385*T)))+A2*(l-(l/&E«*(.0233*T))) 1 4 7 . 6 9 2 0 00090 H=Y+R 70 1 5 1 . 0 8 1 5 00110 PRINT T;H 80 153 . 7666 00120 NEXT T 9 0 1 55 . 8 9 3 6 1 0 0 00130 PRINT ' INPUT DURATION OF RECOVERY' 1 5 7 . 5 7 8 5 OClitO INPUT D 1 10 1 5 8 . 9 1 3 1 120 00150 PRINT 'TIME HEART RATE' 1 5 9 . 9 7 0 4 00160 A?--,35*B INPUT DURATION OF ■RECOVERY 7 0 0 1 7 0 FOR T=O TO D S TE P 10 120 COIEO Y1=A.3«&E**(-.026«T) TIME HEART RATE 00190 H=Y1+R 10 1 5 9 . 6 0 0 0 00210 PRINT T*1D;H 20 1 4 0 . 4 5 9 9 00220 NEXT T 30 1 2 ' . 7 0 1 9 0 0 2 5 0 END 40 ir. .3227 EDIT 5 0 1 0 5 . 5 4 8 8 to 60 9 8 . 7 8 3 6 5 ro 70 9 5 . 5 6 7 5 7 VO 80 8 9 . 5 4 5 3 5 9 0 8 5 . 4 4 4 1 7 1 0 0 84 . 0 5 2 9 9 110 8 2 . 2 0 9 2 7 1 2 0 8 0 . 7 8 7 6 6 130 7 9 . 6 9 1 5 3 EDIT r u n W = -watts D = duration in seconds R = RHR B = expected bpm above RHR at SS AI,A2 = fast and slow components Y = bpm above RHR for increasing HR H = HR at time T A3 = fraction of B used for recovery Y1 = bpm above resting for recovery APPENDIX 10 PROGRAM TO PREDICT HEART RATE PATTERNS USING SUGGS' MODEL (BASIC). 7 1 00050 PRINT ' INPUT 1 FOR EXERCISE, 2 FOR RECOVERY, AND 3 FOR STOP' ENTER WATTS, DURATION 00055 T1=0 ? 100,2,72 00060 INPUT X TIME H E A R T RATE 00068 IF X=1 THEN 100 0 72 00070 IF X=2 THEN UOO 10 81.81345 00072 IF X=3 THEN 500 20 90,55685 00100 PRINT 'ENTER WATTS, DURATION IN MINUTES, AND.RHR' 30 • 98.34688 00110 INPUT H,D,R 40 105.2875 00112 0=.01i»*W 50 111.4713 00111» 5=60*0+78 60 115.9809 00120 A=S-R 70 121.8897 00130 PRINT 'TIME HEART RATE* 80 126.2632 OOUtO FOR T=0T0DSTEP.1666 90 130. 1599 00150 H=S-A*(&E**(-.593*T)> 100 133.6316 00160 PRINT T1;H 110 136.7249 00164 T1=T1+10 120 139.4808 00170 NEXT T DO YOU WISH ANOTHER 00172 GO TO 480 ? 'yes ' 00400 PRINT INPUT 1 FOR EXERCISE, 00410 PRINT 'INPUT SS FOR EXERCISE, DURATION, IV ? 2 00420 INPUT S,D,I 00430 A=I-S INPUT SS FOR EXERCISE, 00440 FOR T-OTODSTEP.1B66 ? 72,2,150 00450 H=S+A*(&E**(-.499*T)) 0 150 00460 PRINT T1;H 10 143.7778 to 00464 T1«=T1+10 20 138.0520 to 00470 NEXT T 30 132.7829 00480 PRINT ' DO YOU WISH ANOTHER* 40 127,9342 00490 INPUT A$ 50 123.4722 00495 IF A$-*Y£S* THEN 50 60 119.3662 00500 END 70 115.5877 EDIT 80 112.1107 90 108.9110 100 105.9665 110 103.2570 T l = time periods in seconds 120 100.7636 = DO YOU WISH ANOTHER X i n d i c a t o r ? •yes ' w : - watt s D = duration in minutes R = RHR 0 — oxygen consumption S SS H R T =: time periods in minutes H = HR at time Tl S = expect SS for exercise D duration in minutes I IV APPENDIX 11 PROGRAM TO PREDICT HEART RATE PATTERNS USING VOGT'S MODEL (BASIC). ENTER 1 IF INCREA 2 IF DECREASE 7 1 ENTER WATTS, DURA IV AND RHF. 7 00010 PRINT 'ENTER 1 IF INCREASE AND 2 IF DECREASE' 220,2,76,76 00020 INPUT Cl TIME HEART RATE 00050 PRINT 'ENTER WATTS, DURATION IN MINUTES, IV AND RHR' 0 80.29 182 0001*0 INPUT V/,D, l,R 1 0 109 . 9 916 00050 C=.U»W 2 0 129.1559 00065 T1=0 30 11*1 .5173 00070 IF Cl=l THEN 200 1*0 11* 9.1*9 1*2 OOOSO K=-.712-.00G9*C 50 151*.61*09 00050 GO TO 220 50 157.9615 00200 K=-1.35-.0078*(l+C) 70 160.101*0 00220 PRINT 'TIME HEART RATE' 80 161 . 1*863 • 00230 FOR T=OTOD STEP .165666 90 162.3781 00235 Pl=-K*T+.05 1 0 0 162.9536 00236 P2 = l/f*E**Pl 1 1 0 163 .321*8 00237 H=C*(1-P2) 1 2 0 163 .561*1* EDIT n n 0021*0 IF Cl = l THEN 21*8 ro 0021*2 Hl=l-H NJ 0021* 1* GO TO 250 0021*8 lll = H*R 00250 PRINT T1;H1 ENTER 1 IF INCREASE AND 2 IF DECREASE 00252 T1=T1+10 7 2 00260 NEXT T ENTER WATTS, DURATION IN MINUTES, IV AND RHR 00270 END ? 220, 2, 161*, 76 [0!T TIME HEART RATE 0 159.7082 01 - indicator 10 11*3 1861* W = watts 20 129 0256 D = duration in minutes 30 119 .2821 I = IV 1*0 110 . 7301* 50 103 . 8823 R = RHR 60 98 . 3791*7 C = expected bpm above RHR at SS 70 93 96239 Tl = time periods in seconds 80 90 1*1711 K = time constant 90 87 57158 T = time periods in minutes 100 85 2S7G6 110 83 1*51*51* P1,P2 = dummy.variables 120 81 H = bpm above RHR EDIT run HI = predicted HR APPENDIX 12 PROGRAMS TO DETERMIN]E SIGNIFICAN CE OF THE DIFFERENCE BETWEEN REGRESSION onolo A1 = 0 COEFFICIENTS OF TWO SEPARATE EQUATIONS (BASIC). 00020 A2=0 00030 PRINT' INPUT N* 00010 PR IMT ' IN PUT SYIX 3X1 M1 SY 2X 3X2 N 2 ' 00040 INPUT N 00020 1 NPUT SI, XI, NX,32, X2,N2 00050 FOR |=1T0N 00030 S3 = ((N 1-2 )*3 1+(N2- 2 )*S2 )/(N 1 + M2-4 ) 00055 INPUT X,Y 00040 34 =33* (1/ ((N 1-1)*X 1) + 1/ ((N2 -1) *X2)) 00060 A1=A1+Y 00050 35 = 84* *.5 00070 A2=A2+Y**2 00060 PR INI ' INPUT 81 AND 82 ' 00080 B1=B1+X 00070 INPUT Bl, 82 00090 B2=B2+X**2 00080 T= (81- 82) /S5 00100 NEXT 1 00090 PR INT •T FOR Bl AND 82 OF', Bl; 82 00110 PRINT 'INPUT SLOPE' 00100 PR INT 'T= •;T 00120 INPUT S 00110 END 00130 S1=(N*B2-B1* *2)/(N*(N -D) EDIT 00140 S2=(N*A2-A1* *2)/(N*(N -D) 00150 S3=((N-1)/(N -2))*(32- (3**2)*31) ro 00160 PRINT 'SX','SY', 'SYX' 00170 PRINT 31,32, S3 00180 END EDIT Program to compute sums of squares Program to calculate t statistic N = number of observation S1,S2 ^y/xl’ ^y/x2 X,Y = values of independent and XI, X2 = s xl ’ x 2 dependent variables A1,A2,B1,B2 = accumulators N1,N2 number of observation (1 and 2 ) S = regression coefficient B1,B2 regression coefficients (I and 2 ) SI,S2,S3 = T computed t ’^x/y (Crow, 1 9 6 1 , p. 1 6 0 ) APPENDIX 13 PROGRAM TO LIST ALL HARD DATA BY TASK (WATFIV). Ihib Pi^OoRAM I. loTS ALL HA*0 DATA ÜY TASK 1 0 IX.ENS I UN M (4,i z or 100 1=1,4 3 DU lie J = 1, 15 4 5, K 5 ) I ;-i{ I 5 105 rCRlA r (4X, Ifl14) e 1 10 IMUE 7 100 uT.ir INUF 8 nc 210 J = l", 16 9 1.35 i t = l 10 WR IT F( 6 , 140 ) 1 1 140 Vi'Kf'AT ( 1111 , '...T I KALE :EMALL 12 w R i T F ( u , 1 5 L ) 13 15^ FCRiNAT I IX , ' r.üHü SECEXTAPF 14 WR112(6,195) I 5 155 FU?!- AT ( IX,' ' ) 1 6 nu 300 K = i,ia 17 aRITc{4,16") I f 3,J,K) lb IfO F TRY AT I 2X, 13,4X 19 IT = I T + i. 0 2 J 200 ÜCMTINUE 2 1 2 10 COM I NJ E ? 2 r rr> 2 3 c N D M 4xl6xl8 ..matrix I subj.ec.t categories J tasks K time periods 227 APPENDIX PROGRAM TO COMPUTE HEART RATE— %RHR CONVERSION TABLE FOR RESTING HEARTS OF 50 TO 90 BEATS/MINUTE (BASIC). TABLE SHO\\TSf IN PART. RHR 70 RHR 72 RHR 7 4 RHR 76 RHR 78 HPM 'G RHR liPH %R!IR 6 PH ■jRHR CPf' 'sRHR 6 P r 'iRHR SO 71 50 69 50 63 50 GO 50 52 74 52 72 52 7 0 52 68 52 8 7 Sit 77 54 75 5 4 7 3 54 71 5 4 69 o SG 80 56 78 5 6 76 56 74 5 6 72 rH S8 83 58 81 58 78 58 76 58 74 GO 86 GO 83 60 81 GO 79 6 6 77 Ü2 89 62 86 62 84 62 62 79 + Git 91 04 80 64 36 04 8 4 6 4 32 '-r. GG 9 4 G G 9 2 60 89 66 87 6 6 35 Ü8 97 68 94 68 92 68 89 6 8 87 7 0 100 70 97 70 95 7 0 9 2 70 90 -J 72 103 7 2' 100 72 97 72 95 72 92 7 k 106 7 4 103 74 100 74 97 74 95 o 7 G 109 76 10 6 7 0 103 76 100 76 97 Ht 78 111 78 108 78 105 78 103 73 100 U GO 114 80 111 GO 108 20 105 80 103 cn 82 117 82 114 o2 111 82 108 82 105 J. Git 120 5 4 117 34 114 84 111 8 4 108 1;^ 86 123 86 119 80 116 86 113 3 6 110 “3 88 126 88 12 2 88 119 38 l i e S3 113 cc 90 129 90 125 90 122 90 11,8 90 115 D HI s 92 131 92 128 92 124 92 1 21 92 118 o'C' C 9lt 134 94 131 94 127 9 4 124 94 121 cc rH 9G 137 96 153 90 13 0 96 126 96 123 X Ht Hù cc a . 93 140 93 136 98 152 98 129 93 126 cn iUO 143 100 139 10 0 15 5 10 0 152 100 12 8 1 102 14C 102 142 102 13? 102 134 102 131 lOlt 149 104 144 104 141 104 137 104 133 cc r. ■~r 106 I S l 10 6 147 100 143 106 139 106 135 X cc ur -H> 108 154 108 tt o-? 150 103 146 103 142 103 133 cc -J 110 157 110 153 110 149 110 145 110 141 X - 112 160 112 156 112 151 112 147 112 144 cc cc O ■tc l i l t 153 114 153 114 154 1 14 150 114 146 cn rH HC • • I I G IGG 116 161 116 157 1 16 153 116 149 118 109 118 164 118 159 113 155 118 151 CM 120 171 120 167 120 162 120 158 120 154 cc X 122 174 12 2 159 122 103 122 ' 1 0 1 122 156 ex UJ ttt. 124 177 124 172 124 168 124 103 124 159 ■3 126 130 126 175 120 170 126 106 12 5 162 + cc . 128 183 123 178 128 173 128 103 128 164 N cc S i -3 J ISO 180 130 181 130 176 130 171 UJ cn 130 167 + O 132 189 132 183 132 178 132 174 132 O 109 rH 134 191 134 18 5 134 181 134 176 134 172 13 G 194 13G 189 130 134 13 6 179 + cx 13 6 174 5 1 38 197 138 192 133 186 138 182 138 177 cc n . ~3 140 200 140 194 140 189 140 184 140 1 /9 — cc Z — cc 0. O cn I = RHR - O J = beats/minute Cn O O CD O =: CD U-%.3 (/) u; (/) D o: LAo I/)3 m I 1 ' 1 —II C: H- »- “D II H- "3 H-H — 1I o u: c: CD o: o a ■<» uj D:ci: ccr-mci: c U.CL “ CL “ CL u_ CL “ Z 3 -CL LL CL Ou CL û-C*.CLCLQ.CLCLa-D_Û.CLZUl Of O C D O O O LA O O O O O O O rH CMfA.rLAorv.oO Cl 0»- 228